Algebra final
2x² - 18
(2x - 6)(x + 3)
-3y + 4
(4y + 5) + (-7y - 1)
x² + 11x + 28
(x + 4)(x + 7)
Yes, it is linear.
Is 3x - 4y = 16 linear? (Lesson 3.1)
x + y = 16 and x - y = 2
The sum of 2 numbers is 16. The difference of those two number is 2. Find the system: (Lesson 6.3)
x = {-3, -1}
What are the roots of the graph shown?
1/2
What is the amount of change in this sequence: 100, 50, 25, 12.5
(0, 1)
What is the vertex in the graph shown?
620
A hippo weighs 600 pounds. It gains 4 pounds each year. How much will the hippo weigh in 5 years? (The label is missing on the answer on purpose :))
y=600+4x
A hippo weighs 600 pounds. It gains 4 pounds each year. Write the equation for the hippo's weight.
1021
A population of 800 beetles is growing at a rate of of 5% each month. How many beetles will there be in 5 months?
1437
A population of 800 beetles is growing at a rate of of 5% each month. How many beetles will there be in a year?
y = 800(1.05)^x
A population of 800 beetles is growing at a rate of of 5% each month. Write an equation to model the population of beetles in x months.
192-3√21
A rectangle is 5√7+2√3 meters long and 6√7-3√3 meters wide. Find the area of the rectangle in simplest form.
22√7-2√3
A rectangle is 5√7+2√3 meters long and 6√7-3√3 meters wide. Find the perimeter of the rectangle in simplest form.
arithmetic sequence
A sequence in which each term is found by adding a fixed amount to the previous term
Stretch of f(x) = x² narrower than the graph of f(x)=x²
Describe how the graph of g(x)=7x² is related to the graph f(x)=x²
Translation of f(x)= x² up 2 units
Describe how the graph of g(x)=x²+2 is related to the graph f(x)=x²
Translation of f(x)=x² down 8 units
Describe how the graph of g(x)=x²-8 is related to the graph f(x)=x²
1/5
Determine the common ratio: 500, 100, 20
no real solutions
Determine the number of real solutions for a quadratic with discriminant of -64
1 real solution
Determine the number of real solutions for a quadratic with discriminant of 0
2 real solutions
Determine the number of real solutions for a quadratic with discriminant of 4
yes; constant; monomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial. -32
yes; quadratic; trinomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial. 2c² + 8c + 9 - 3
yes; linear; monomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial. 3x/7
Not a polynomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial. 5x² -3x⁻⁴
yes; cubic; binomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial. 7a²b + 3b² - a²b
Yes; quadratic; binomial
Determine whether the expression is a polynomial. If it is, find the degree and determine whether it is a monomial, binomial or trinomial: 5mt + t²
wide graph
Does f(x) = 0.25|x| have a narrow or wide graph?
wide graph
Does f(x) = 0.5|x| have a narrow or wide graph?
narrow graph
Does f(x) = 2|x| have a narrow or wide graph?
narrow graph
Does f(x) = 3|x| have a narrow or wide graph?
y=64(0.5)^x
Each year the YMCA hosts a lacrosse tournament. There are 64 teams to start the tournament. During each round half of the teams are eliminated. Which equation models the situation?
0
Evaluate the expression if a = 2, b = 3, and c = -4. 3a² + 3c (Lesson 1.2)
6
Evaluate the expression if a = 2, b = 3, and c = -4. 3a² - 2b (Lesson 1.2)
7
Evaluate the expression if a = 2, b = 3, and c = -4. 4a² - 3b (Lesson 1.2)
47
Evaluate the expression if a = 2, b = 3, and c = -4. a² + b³ + c² (Lesson 1.2)
35
Evaluate the expression if a = 2, b = 3, and c = -4. b³ + a³ (Lesson 1.2)
Exponential Decay
Exponential Growth or Decay?
Growth or decay? y = (1/3)(5/2)ⁿ
Growth
1
How many roots / solutions does a quadratic equation have if the vertex is on the x-axis?
2
How many roots / solutions does a quadratic equation that opens down with a vertex of (2, 4) have?
0 or No real solution
How many roots / solutions does a quadratic equation that opens up with a vertex of (2, 4) have?
Minimum
If a quadratic equation opens upward, is the vertex a maximum or minimum?
30
If a smoothie uses 3 strawberries for every 5 blueberries, how many blueberries are used with 18 strawberries? (Lesson 2.6)
15
If f(x) = x² - 2x, find f(-3) (Lesson 1.7)
3
If f(x) = x² - 2x, find f(3) (Lesson 1.7)
2x + 2y
If the perimeter of the triangle is 10x + 5y, and the measures of two sides are 5x - y and 3x + 4y, Find the measure of the third leg. Hint: Add the 2 sides together and subtract from the perimeter!
infinitely many
If two equations are for the exact same line, there are _______________ solutions. (Lesson 6.1)
no
If two lines are parallel, there is _______ solution. (Lesson 6.1)
one
If two lines intersect each other, there is ______ solution. (Lesson 6.1)
25 cent increase per year
In 2008, a sandwich cost $6.00. In 2018, a sandwich cost $8.50. What was the rate of change? (Lesson 3.3)
10 cent increase per year
In 2010, milk cost $2.50. In 2015, milk cost $3.00. What was the rate of change? (Lesson 3.3)
a
In the expression ax² + bx + c, which value determines how the parabola opens?
No, it is not linear.
Is 3xy - 7 = 10 linear? (Lesson 3.1)
x
Is the axis of symmetry the x value of the vertex or the y value of the vertex
Minimum
Is the vertex for the quadratic equation x² - 4x + 6 = 0 a max or a min?
Yes, it is linear.
Is y = x linear? (Lesson 3.1)
No, it is not linear.
Is y = x² linear? (Lesson 3.1)
y=64(3)^x
Mary finds 64 crickets in her garage. Every day the crickets triple in population. Which equation models the situation?
12x² + 29x - 8
The Loft Theater has a center seating section with 3x + 8 rows and 4x - 1 seats in each row. Write an expression for the total number of seats in the center section.
l = A/w
The area formula for a rectangle is A = lw. What is the formula for l? (Lesson 2.8)
w = A/l
The area formula for a rectangle is A = lw. What is the formula for w? (Lesson 2.8)
same slope
Parallel means equations have the (Lesson 4.4)
negative reciprocal slopes
Perpendicular means equations have the (Lesson 4.4)
standard form
The equation 2x - 5y = 10 is written in (Lesson 3.1)
standard form
The equation 4x + 3y = 11 is written in (Lesson 3.1)
point-slope form
The equation y + 2 = -4(x + 5) is written in (Lesson 4.3)
point-slope form
The equation y - 3 = 4(x + 3) is written in (Lesson 4.3)
slope-intercept form
The equation y = 2x - 5 is written in (Lesson 4.2)
slope-intercept form
The equation y = 3x + 1 is written in (Lesson 4.2)
{(4,3), (-2, -1), (2, -4), (0, 4)}
The following mapping contains the points (Lesson 1.6)
x + y = 10 and x - y = 8.
The sum of 2 numbers is 10. The difference of those two number is 8. Find the system: (Lesson 6.3)
y = x + 50
Translate to an equation: A 50 pound dog is gaining 1 pound each month. (Lesson 4.1)
y = -10x + 100
Translate to an equation: A bird at 100 ft descends 10 ft per minute. (Lesson 4.1)
y = -2x + 100
Translate to an equation: A store with 100 pairs of sneakers sells 2 pairs each hour. (Lesson 4.1)
y = 2x + 5
Translate to an equation: The cost of bowling is $2 per game plus $5 for shoes. (Lesson 4.1)
y = 2x - 10
Translate to an equation: The profit of selling lemonade is $2 per cup minus the $10 of supplies. (Lesson 4.1)
x - 2 = y + 5
Translate: Two less than x is equal to 5 more than y. (Lesson 2.1)
x + 2 = y + 5
Translate: Two more than x is equal to 5 more than y. (Lesson 2.1)
x = {-3, 1}
What are the roots of the graph shown?
x = {∅}
What are the roots of the graph shown?
x = {∅} no roots
What are the roots of the graph shown?
y < -1
What inequality is shown in the graph? (Lesson 5.6)
y > -x + 1
What inequality is shown in the graph? (Lesson 5.6)
y ≤ 2x + 4
What inequality is shown in the graph? (Lesson 5.6)
x < 3
What inequality is shown in the graph? (Lesson 5.6)
x = 2
What is the axis of symmetry for the quadratic equation x² - 4x + 6 = 0?
x = 0
What is the axis of symmetry for the quadratic equation y = x² + 2?
x = -1
What is the axis of symmetry in the graph shown?
x = -2
What is the axis of symmetry in the graph shown?
x = 0
What is the axis of symmetry in the graph shown?
3
What is the common ratio? 2, 6, 18, 54..
1/4
What is the common ratio? 64, 16, 4 , 1...
domain: all reals; range: y ≤ -4
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ -1
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ -4
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ 1
What is the domain and range in the graph shown?
f(x) = 2|x|
What is the function of this graph?
f(x) = |x - 2| + 1
What is the function of this graph?
f(x) = |x - 3| - 1
What is the function of this graph?
f(x) = |x|
What is the function of this graph?
f(x) = |x| + 2
What is the function of this graph?
f(x) = |x| - 2
What is the function of this graph?
-2 ≤ x < 3
What is the graph of: (Lesson 5.1)
x > -6
What is the graph of: (Lesson 5.1)
x ≤ -4 or x > 0
What is the graph of: (Lesson 5.1)
x ≤ 6
What is the graph of: (Lesson 5.1)
x ≥ -5
What is the graph of: (Lesson 5.1)
-5
What is the leading coefficient for the polynomial (Hint: first put the polynomial in standard form): 6x - 2x² - 5x³ + 1
-2
What is the leading coefficient of: -2x⁷ - 5x + 8
5
What is the leading coefficient of: 5x⁵ + 8x² - 4
4x + 10
What is the perimeter of a rectangle with a length of x + 2 and a width of x + 3?
6x + 14
What is the perimeter of a rectangle with a length of x + 6 and a width of 2x + 1?
4x + 8
What is the perimeter of a square with a side length of x + 2?
4x - 24
What is the perimeter of a square with a side length of x - 6?
3x - 2y
What is the perimeter of a triangle with side lengths of 2x + 3y, 5x - 6y, and -4x + y?
3x² + 9x
What is the perimeter of an equilateral triangle with a side length of x² + 3x?
Vertex
What is the point at which the parabola begins to change direction?
(2, 2)
What is the vertex for the quadratic equation x² - 4x + 6 = 0?
(0, 2)
What is the vertex for the quadratic equation y = x² + 2?
(-1, -4)
What is the vertex in the graph shown?
(-2, -1)
What is the vertex in the graph shown?
(0, -4)
What is the vertex in the graph shown?
(-4, 5)
What is the vertex of: f(x) = |x + 4| + 5
(2, 0)
What is the vertex of: f(x) = |x - 2|
(4, 0)
What is the vertex of: f(x) = |x - 4|
(4, 5)
What is the vertex of: f(x) = |x - 4| + 5
(4, -5)
What is the vertex of: f(x) = |x - 4| - 5
(5, 4)
What is the vertex of: f(x) = |x - 5| + 4
(5, -4)
What is the vertex of: f(x) = |x - 5| - 4
(0, 0)
What is the vertex of: f(x) = |x|
(0, -2)
What is the vertex of: f(x) = |x| - 2
(0, -4)
What is the vertex of: f(x) = |x| - 4
Create an x / y table.
When graphing a quadratic equation, what is the step that follows finding the vertex?
the rate of change is addition or subtraction by a constant
When looking at a table of values, how can you determine if the table is a linear function?
the rate of change is multiplication or division by a constant
When looking at a table of values, how can you determine if the table is an exponential function?
y = 0.5x + 7
Which equation is parallel to y = 0.5x - 3? (Lesson 4.4)
y = 2.2x + 4
Which equation is parallel to y = 2.2x - 6 (Lesson 4.4)
y = 1/5x + 5
Which equation is perpendicular to y = -5x + 2? (Lesson 4.4)
y = -1/10x + 3
Which equation is perpendicular to y = 10x - 5? (Lesson 4.4)
Down
Will the graph for the quadratic equation f(x) = -2x² + 8x - 3 open up or down?
-3x² - 2x
(-x² + 3x) - (5x + 2x²)
(y₂ - y₁)/(x₂ - x₁)
The slope formula is (Lesson 3.3)
9x - 13y
(11x - 7y) - (2x + 6y)
6x² - 6
(2x + 2)(3x - 3)
4x³ + 12x² + 17x + 12
(2x + 3)(2x² + 3x + 4)
6x + 12y
(2x + 3y) + (4x + 9y)
2x² - 3x - 20
(2x + 5)(x - 4)
4x² + 4xy² + y⁴
(2x + y²)²
4x⁴ + 12x²y² + 9y⁴
(2x² + 3y²)²
3x² + x + 7
(2x² + 6x) + (x² - 5x + 7)
8x⁴ + 8x³ + 10x² + 4x - 6
(2x² + x + 3)(4x² + 2x - 2)
4x⁴ - 12x³ + 8x² + 6x - 9
(2x² - 2x - 3)(2x² - 4x + 3)
-x² + 2x
(2x² - 5x) + (7x - 3x²)
3x² + 7x + 2
(3x + 1)(x + 2)
3x² - 5x - 2
(3x + 1)(x - 2)
9x² - 4
(3x + 2)(3x - 2)
6x³ + 21x² + 9x - 6
(3x + 3)(2x² + 5x - 2)
9x² + 3x - 6
(3x + 3)(3x - 2)
9x² - 49
(3x + 7)(3x - 7)
9x² - 9y²
(3x - 3y)(3x + 3y)
3x² + 2x - 21
(3x - 7)(x + 3)
9x⁴ - 6x³ - 17x² - 18x - 10
(3x² + 2x + 2)(3x² - 4x - 5)
6x⁴ + 7x³ + 27x² + 17x - 9
(3x² + 2x - 1)(2x² + x + 9)
9x⁴ - 6x²y + y²
(3x² - y)²
7x²y³ + 6xy
(3x²y³ + xy) + (4x²y³ + 5xy)
8x² + 6x + 1
(4x + 1)(2x + 1)
8x² + 18xy + 9y²
(4x + 3y)(2x + 3y)
16x² - 12x + 2
(4x - 2)(4x - 1)
-3x² + 3x - 12
(4x² + 2x - 8) - (7x² + 4 - x)
4x² + 6x - 1
(4x² + 8x + 2) - (2x + 3)
3x + 5y
(5x + 9y) - (2x + 4y)
3x + y + 1
(5x + y - 2) + (-2x + 3)
10x² - 19x + 6
(5x - 2)(2x - 3)
-2x² + 13x - 3
(5x² + 6x + 2) - (7x² - 7x + 5)
36 + 12x + x²
(6 + x)²
10x + 13y
(6x + 5y) + (4x + 8y)
42x² - 45x + 12
(6x - 3)(7x - 4)
10x² - 3x + 9
(6x² + 2x + 9) + (4x² - 5x)
4x² - 9x + 5
(6x² - x + 1) - (-4 + 2x² + 8x)
36x⁶ - 12x³y + y²
(6x³ - y)²
5x² + 24x - 5
(x + 5)(5x - 1)
x² + 6x + 5
(x + 5)(x + 1)
x² + 10x + 25
(x + 5)²
x² + 14x + 48
(x + 6)(x + 8)
x² - 2x - 48
(x + 6)(x - 8)
x² + 12x + 36
(x + 6)²
x² + 12x + 35
(x + 7)(x + 5)
x² + 2x - 35
(x + 7)(x - 5)
x² - 49
(x + 7)(x - 7)
x² + 14x + 49
(x + 7)²
x² - 64
(x + 8)(x - 8)
x² + 16x + 64
(x + 8)²
x² + 12x + 27
(x + 9)(x + 3)
x² + 6x - 27
(x + 9)(x - 3)
x² - 81
(x + 9)(x - 9)
x² + 18x + 81
(x + 9)²
x² + 2xy + y²
(x + y)²
5x² - 9x + 4
(x - 1)(5x - 4)
x² + x - 2
(x - 1)(x + 2)
x² + 4x - 5
(x - 1)(x + 5)
x² + 7x - 8
(x - 1)(x + 8)
x² - 3x + 2
(x - 1)(x - 2)
x² - 9x + 8
(x - 1)(x - 8)
x² - 2x + 1
(x - 1)²
x² - 20x + 100
(x - 10)²
x² - 22x + 121
(x - 11)²
x² - 24x + 144
(x - 12)²
x² + x - 6
(x - 2)(x + 3)
x² + 3x - 10
(x - 2)(x + 5)
x² - 4x + 4
(x - 2)(x - 2)
x² - 5x + 6
(x - 2)(x - 3)
x² - 7x + 10
(x - 2)(x - 5)
x² - 4x + 4
(x - 2)²
x² - 7x + 12
(x - 3)(x - 4)
x² - 6x + 9
(x - 3)²
x² + 3x - 28
(x - 4)(x + 7)
x² - 3x - 4
(x - 4)(x +1)
x² - 5x + 4
(x - 4)(x - 1)
x² - 11x + 28
(x - 4)(x - 7)
x² - 8x + 16
(x - 4)²
x² - 8xy + 16y²
(x - 4y)²
x² - 4x - 5
(x - 5)(x + 1)
x² - 25
(x - 5)(x + 5)
x² - 6x + 5
(x - 5)(x - 1)
x² - 10x + 25
(x - 5)²
x² + 2x - 48
(x - 6)(x + 8)
x² - 14x + 48
(x - 6)(x - 8)
x² - 12x + 36
(x - 6)²
x² - 2x - 35
(x - 7)(x + 5)
x² - 12x + 35
(x - 7)(x - 5)
x² - 14x + 49
(x - 7)²
x² - 16x + 64
(x - 8)²
x² - 6x - 27
(x - 9)(x + 3)
x² - 12x + 27
(x - 9)(x - 3)
x² - 18x + 81
(x - 9)²
2x² - 3xy + y²
(x - y)(2x - y)
x = -33
(x/-3) - 6 = 5 (Lesson 2.3)
-x² - 8x
(x² - 3x) - (2x² + 5x)
6x² - 7x - 6
(x² - 4x - 1) + (-5 + 5x² - 3x)
x² - 3x
(x² - x + 5) - (2x + 5)
2x² + x
(x² - x) + (2x + x²)
decreases
exponential decay
increases
exponential growth
x = -16
x/-2 + 1 = 9 (Lesson 2.3)
x = 42
x/7 + 4 = 10 (Lesson 2.3)
x = 56
x/8 + 3 = 10 (Lesson 2.3)
-4x³ - x²
x²(-4x + 5) - 6x²
Decay
y = 223(0.8)^x, growth or decay?
Growth
y = 25(1.32)^x, growth or decay?
6 and -2
|x - 2| = 4, what is x? (Lesson 2.5)
7 and -7
|x| + 4 = 11, what is x? (Lesson 2.5)
13 and -13
|x| - 3 = 10, what is x? (Lesson 2.5)
12 and -12
|x| - 4 = 8, what is x? (Lesson 2.5)
x < -8
2x + 4 < -12 (Lesson 5.3)
x < -15
2x > -30 (Lesson 5.2)
-14x³ - 8x²
2x(-7x² - 4x)
2x² - 8x
2x(x - 4)
2x²y² + 2x²y³
2xy(xy + xy²)
6x² + 6x - 3
3x(3x + 6) - 3(x² + 4x + 1)
3√7 - 9√21 / 26
3√7 / (-1-√27)
-22x² + 2x + 8
4x(-5x - 3) - 2(x² - 7x - 4)
x < -6
5x < -30 (Lesson 5.2)
-4x³ + 3x² + 19x
5x(-7x + 3) + 2x(-2x² + 19x + 2)
15x²y² + 10xy²
5xy(3xy + 2y)
2x² - 63x + 15
6x(2x - 3) - 5(2x² + 9x - 3)
18x³y + 24xy²
6xy(3x² + 4y)
x > 8
8x - 6 > 6x + 10 (Lesson 5.3)
36√6
Simplify 4√3 × 3√18
(5√7 - 5√3) / 4
Simplify 5 / (√7+√3)
-3√19+11√7
Simplify 5√19+4√28-8√19+√63
6√2+6√5
Simplify 5√8+3√20-√32
-5√13x
Simplify 7√13x -14√13x +2√13x
(12-4√3)/3
Simplify 8 / (3+√3)
4√30
Simplify 8√30 - 4√30
3x² + 7x
Simplify x(3x + 2) + 5x
√11/11
Simplify √(1/7) × √(7/11)
3√2x / x²
Simplify √(18/x³)
√5 / 5
Simplify √(2/10)
√15 / 5
Simplify √(3/4) × √(4/5)
6√3
Simplify √108
6|x³|y²√3
Simplify √108x⁶y⁴
2√6
Simplify √24
3√2+13√3
Simplify √27+√18+√300
3|x|√3xy
Simplify √27x³y
√6k / 4
Simplify √3k /√8
4√10
Simplify √40-√10+√90
-3√10
Simplify √5(5√2-4√8)
5x²√2x
Simplify √50x⁵
2|x|y²√14y
Simplify √56x²y⁵
2√15+3√10
Simplify √6(√10+√15)
2√15
Simplify √60
7√2
Simplify √7 × √14
2√3 / 3
Simplify √8 / √6
4√3
Simplify √8 × √6
The population is growing at a rate 2.2% each year.
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. What does 1.022 mean?
The population of the city in 1980
Since January 1980, the population of a city has grown according to the model, where x represents the number of years since January 1980. What does 720,500 represent?
y = -2/3x + 2
Solve 2x + 3y = 6 for y. (Lesson 2.8)
y = -4/3x + 2
Solve 4x + 3y = 6 for y. (Lesson 2.8)
{-9.9, -0.1}
Solve by completing the square. Round to the nearest tenth if necessary: 2x²+20x=-2
{-11, -1}
Solve by completing the square. Round to the nearest tenth if necessary: x²+12x+21=10
{2, -6}
Solve by completing the square. Round to the nearest tenth if necessary: x²+4x-12=0
{-7, 1}
Solve by completing the square. Round to the nearest tenth if necessary: x²+6x=7
{2. 12}
Solve by completing the square. Round to the nearest tenth if necessary: x²-14x+30=6
{-3, 5}
Solve by completing the square. Round to the nearest tenth if necessary: x²-2x=15
{-1.4, 3.4}
Solve by completing the square. Round to the nearest tenth if necessary: x²-2x=5
{0.3, 3.7}
Solve by completing the square. Round to the nearest tenth if necessary: x²-4x+1=0
{0.8, 5.2}
Solve by completing the square. Round to the nearest tenth if necessary: x²-6x+4=0
{1.6, 6.4}
Solve by completing the square. Round to the nearest tenth if necessary: x²-8x+10=0
{3, 5}
Solve by completing the square. Round to the nearest tenth if necessary: x²-8x+15
{-3½, 1}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary 2x²+5x-7=0
∅
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²+5x+4=0
{-4½, 1}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²+7x=9
{½, 1}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 2x²-3x=-1
{-1.4, 0.7}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 3x²+2x-3=0
{-2/3, 3}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: 3x²-7x-6=0
{-7, 7}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x² - 49=0
{-4, 9}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x² - 5x - 36=0
{-4, 5}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x² - x - 20=0
{-6, -5}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+11x+30=0
{-3.7, -0.3}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+4x=-1
{-5.4, -0.6}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²+6x+3=0
{0.5, 6.5}
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-7x=-3
no real solutions
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary: x²-9x+22=0
all real numbers
Solve the equation 3x + 7 = 7 + 3x (Lesson 2.4)
no solution
Solve the equation 3x - 4 = 3x + 5 (Lesson 2.4)
y = -24
Suppose y varies directly as x, and y=-12 when x = 2. Find y when x = 4. (Lesson 3.4)
y = 15
Suppose y varies directly as x, and y=10 when x = 2. Find y when x = 3. (Lesson 3.4)
x = 4
Suppose y varies directly as x, and y=20 when x = 5. Find x when y = 16. (Lesson 3.4)
x = 3
Suppose y varies directly as x, and y=36 when x = 4. Find x when y = 27. (Lesson 3.4)
489.22
You buy a $600 art piece that loses 4% of it's value each year. How much will that piece be worth in 5 years?
y=600(.96)^x
You buy a $600 art piece that loses 4% of it's value each year. Write the equation for the situation.
729.99
You have $600 in an account. Each year, you gain 4% just for having money in there. How much money will you have in 5 years?
y=600(1.04)^x
You have $600 in an account. Each year, you gain 4% just for having money in there. Write the equation for the situation.
y=64(2)^x
You have $64 in your savings account and you want to double the amount every year. Which equation models the situation?
23329.97
Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return?
306.62
Your new computer was worth $1500 but it depreciates in value by 18% each year. How much will your computer be worth (to the nearest penny) after 8 years?
y = 1500(.82)^t
Your new computer was worth $1500 but it depreciates in value by 18% each year. Write an equation to model the value of the computer after t years.
Geometric sequence
a sequence in which each term is found by multiplying the previous term by the same number
13, 952.30
$13,500 deposit earning 3.3% compounded monthly after 1 year
634.87
$500 principal earning 4% compounded quarterly after 6 years
5229.70
$5000 deposit earning 1.5% compounded quarterly after 3 years
x² + 3x + 2
(x + 1)(x + 2)
x² + 9x + 8
(x + 1)(x + 8)
x² - x - 2
(x + 1)(x - 2)
x² - 7x - 8
(x + 1)(x - 8)
x³ + 3x² + 6x + 4
(x + 1)(x² + 2x + 4)
x² + 2x + 1
(x + 1)²
x² - 100
(x + 10)(x - 10)
x² + 20x + 100
(x + 10)²
x² + 22x + 121
(x + 11)²
x² + 24x + 144
(x + 12)²
x² + 4x + 4
(x + 2)(x + 2)
x² + 5x + 6
(x + 2)(x + 3)
x² + 7x + 10
(x + 2)(x + 5)
x² - 4
(x + 2)(x - 2)
x² - x - 6
(x + 2)(x - 3)
x² - 3x - 10
(x + 2)(x - 5)
x² + 4x + 4
(x + 2)²
x² + 7x + 12
(x + 3)(x + 4)
x² - 9
(x + 3)(x - 3)
x² - x - 12
(x + 3)(x - 4)
x³ + 6x² + 14x + 15
(x + 3)(x² + 3x + 5)
x² + 6x + 9
(x + 3)²
x² + 6xy + 9y²
(x + 3y)²
x² + 5x + 4
(x + 4)(x + 1)
x² + 3x - 4
(x + 4)(x - 1)
x² + x - 12
(x + 4)(x - 3)
x² - 16
(x + 4)(x - 4)
x² - 3x - 28
(x + 4)(x - 7)
x³ + 7x² + 6x - 24
(x + 4)(x² + 3x - 6)
x² + 8x + 16
(x + 4)²
x² + 8xy + 16y²
(x + 4y)²
9x² - 7x - 12
-2(3x³ + 5x + 6) + 3x(2x² + 3x + 1)
6n⁴ - 2n³ - 4n²
-2/3 n²(-9n² + 3n + 6)
6n⁴ - 9n³ - 12n²
-3n²(-2n² + 3n + 4)
-3x² + 3x + 3
-3x(7x - 2) + 3(x² + 2x + 1) - 3x(-5x + 3)
-3x³ - 6x²
-3x(x² + 2x)
-4x + 36x² + 8x³
-4x(1 - 9x - 2x²)
-11x² - 4x
-x(11x + 4)
-2x² + 3x
-x(2x - 8) - 5x
ratio
1/2, 1 to 2, and 1:2 are all ways to show a (Lesson 2.6)
2 + (x - 7) = x - 4
2 plus the difference of x and 7 is equal to x subtracted by 4. (Lesson 2.1)
2 + (x + 7) = x - 4
2 plus the sum of x and 7 is equal to x subtracted by 4. (Lesson 2.1)
100 - 100(0.20)
A $100 tablet with 20% off would be calculated like this: (Lesson 2.7)
$106
A $100 tablet with 6% sales tax would cost (Lesson 2.7)
100 + 100(0.08) =
A $100 tablet with 8% sales tax would be calculated like this: (Lesson 2.7)
$4.24
A $4.00 item has 6% sales tax. What is the price? (Lesson 2.7)
580
A tiger weighs 600 pounds. It loses 4 pounds each year. How much will the tiger weigh in 5 years?(The label is missing on the answer on purpose :))
y=600-4x
A tiger weighs 600 pounds. It loses 4 pounds each year. Write the equation for the tiger's weight.
$7.20
An $8.00 item is discounted 10%. What is the price? (Lesson 2.7)
$6.40
An $8.00 item is discounted 20%. What is the price? (Lesson 2.7)
$4.80
An $8.00 item is discounted 40%. What is the price? (Lesson 2.7)
Growth or decay? y = -2(4/7)ⁿ
Decay
Translation of f(x)=x² down 2/5 units
Describe how the graph of g(x) = x² - 2/5 is related to the graph f(x)=x²
Reflection of f(x)=x² across the x-axis translated up 9 units
Describe how the graph of g(x)= -x² + 9 is related to the graph f(x)=x²
Compression of f(x)=x² wider than the graph of f(x)=x², reflected over the x-axis, translated down ½ unit.
Describe how the graph of g(x)= -¾x² - ½ is related to the graph f(x)=x²
Stretch of f(x) = x² narrower than the graph of f(x) translated up 2 units.
Describe how the graph of g(x)= 2x² + 2 is related to the graph f(x)=x²
Translation of f(x)=x² to the left 10 units
Describe how the graph of g(x)=(x + 10)² is related to the graph f(x)= x²
Translation of f(x)=x² to the right one unit
Describe how the graph of g(x)=(x-1)² is related to the graph f(x)=x²
Stretch of f(x)=x² narrower than the graph of f(x)=x², reflected over the x-axis translated to the left 4 units.
Describe how the graph of g(x)=-3(x + 4)² is related to the graph f(x)=x²
Stretch of f(x)=x² narrower than the graph of f(x)=x² reflected over the x-axis.
Describe how the graph of g(x)=-6x² is related to the graph f(x)=x²
Reflection of f(x)=x² over the x-axis translated up 3 units
Describe how the graph of g(x)=-x²+3 is related to the graph f(x)=x²
Compression of f(x)=x² wider than the graph of f(x)=x² reflected over the x-axis translated up 5 units.
Describe how the graph of g(x)=-½x² + 5 is related to the graph f(x)=x²
Compression of f(x)=x² wider than the graph of f(x)=x²
Describe how the graph of g(x)=1/5 x² is related to the graph f(x)=x²
Stretch of f(x)=x² narrower than the graph of f(x)=x² translated to the right 1 unit
Describe how the graph of g(x)=4(x-1)² is related to the graph f(x)=x²
486
Find a(6) for the given sequence: 2, 6, 18...
16,661.35
Find the balance in the account after the given period. $12,000 principal earning 4.8% compounded annually after 7 years
-1/3
Find the common ratio of the sequence: 81, -27, 9
4
Find the common ratio: 1, 4, 16, 64
-64
Find the discriminant 2x²-4x+10=0
89
Find the discriminant for 2x²+5x-8=0
-60
Find the discriminant for 2x²+6x+12=0
13
Find the discriminant for 3x²+7x+3=0
0
Find the discriminant for x²+2x+1=0
4
Find the discriminant for x²+4x+3=0
32
Find the discriminant for x²-2x-7=0
-24
Find the discriminant for x²-4x+10=0
8
Find the discriminant for x²-6x+7=0
1, -4, 16, -64, 256
Find the first five terms of the sequence: t(n) = 1(-4)ⁿ⁻¹
10, -40, 160,
Find the first three terms of the sequence: a(n)= 10(-4)ⁿ⁻¹
11, 9, 14
Find the next 3 terms in the sequence: 1, 5, 3, 8, 6, ... (Lesson 3.5)
16, 19, 22
Find the next 3 terms in the sequence: 4, 7, 10, 13, ... (Lesson 3.5)
-15, -20, -25
Find the next 3 terms in the sequence: 5, 0, -5, -10, ... (Lesson 3.5)
243, 729, 2217
Find the next three numbers 3, 9, 27, 81
-192, 768, -3072
Find the next three terms of the sequence: 3, -12, 48
66.7% decrease
Find the percent of change from $1.50 to $0.50. (Lesson 2.7)
25% increase
Find the percent of change from $4 to $5. (Lesson 2.7)
75% decrease
Find the percent of change from $4.00 to $1.00 (Lesson 2.7)
200% increase
Find the percent of change from $5 to $15. (Lesson 2.7)
-3/5
Find the slope between the points (-4, 8) and (6, 2) (Lesson 3.3)
0
Find the slope between the points (5, 8) and (4, 8) (Lesson 3.3)
100
Find the value of c that makes x²+20x+c a perfect square trinomial
4
Find the value of c that makes x²+4x+c a perfect square trinomial
6.25
Find the value of c that makes x²+5x+c a perfect square trinomial
9
Find the value of c that makes x²+6x+c a perfect square trinomial
20.25
Find the value of c that makes x²+9x+c a perfect square trinomial
30.25
Find the value of c that makes x²-11x+c a perfect square trinomial
49
Find the value of c that makes x²-14x+c a perfect square trinomial
81
Find the value of c that makes x²-18x+c a perfect square trinomial
1
Find the value of c that makes x²-2x+c a perfect square trinomial
1225
Find the value of c that makes x²-70x+c a perfect square trinomial
Changing a % into a decimal
Move the decimal two spaces to the left
22.5 feet
On a map, if 2 inches equals 4.5 feet, how many feet does 10 inches represent? (Lesson 2.6)
2√30+30√2
Simplify (4√3-2√5)(3√10+5√6)
40-10√15
Simplify (5-√15)²
4√3
Simplify (√10+√6)(√30-√18)
30√3-5√10
Simplify (√2+2√8)(3√6-√5)
36+14√6
Simplify (√8+√12)(√48+√18)
14√2
Simplify 2√32 + 3√50 - 3√18
14√5
Simplify 2√45 + 4√20
-10√5
Simplify 2√5-7√5-5√5
12√21+20√14
Simplify 2√7(3√12+5√8)
(15+3√2)/23
Simplify 3 / (5-√2)
-√10-3√3
Simplify 3√10+√75-2√40-4√12
90√2
Simplify 3√12 × 5√6
{(-2, 3), (-3, -2)}
The inverse of {(3, -2), (-2, -3)} is (Lesson 4.7)
{(3,4), (-1, -2), (-4, 2), (4, 0)}
The inverse of {(4,3), (-2, -1), (2, -4), (0, 4)} is: (Lesson 4.7)
Axis of Symmetry
The line that splits a quadratic equation at the point of symmetry is called
2
The minimum number of points needed to graph a line is
difference/original
The percent of change formula is (Lesson 2.6)
x-intercept
The point where the line crosses the x-axis is called the (Lesson 1.8)
y-intercept
The point where the line crosses the y-axis is called the (Lesson 1.8)
y = 2x - 4
Write in slope-intercept form: 2x - y = 4 (Lesson 4.3)
y = -3x + 6
Write in slope-intercept form: 3x + y = 6 (Lesson 4.3)
y = 3/2x - 3
Write in slope-intercept form: 3x - 2y = 6 (Lesson 4.3)
y = -1/4x + 2
Write in slope-intercept form: x + 4y = 8 (Lesson 4.3)
3x - y = 11
Write in standard form: y + 2 = 3(x - 3) (Lesson 4.3)
3x - y = -5
Write in standard form: y - 2 = 3(x + 1) (Lesson 4.3)
2x - y = -5
Write in standard form: y - 3 = 2(x + 1) (Lesson 4.3)
x + (x + 2) + (x + 4) = -42
Write the equation for: three consecutive EVEN integers have a sum of -42. (Lesson 2.1)
x + (x + 2) = -42
Write the equation for: two consecutive EVEN integers have a sum of -42. (Lesson 2.1)
x + (x + 2) = 42
Write the equation for: two consecutive ODD numbers have a sum of 42. (Lesson 2.1)
x + (x + 1) = 41
Write the equation for: two consecutive integers have a sum of 41. (Lesson 2.1)
x + (x + 1) = 42
Write the equation for: two consecutive integers have a sum of 42. (Lesson 2.1)
y = 1/2x + 5
Write the equation of the line that passes through (-4, 3) and (2, 6) (Lesson 4.2)
y = 2x + 3
Write the equation of the line that passes through (0, 3) and (3, 9) (Lesson 4.2)
-x³ + x + 25
Write the polynomial in standard form: 25 - x³ + x
5x⁵ + 8x² - 15
Write the polynomial in standard form: 8x² - 15 + 5x⁵
x < 6
x + 4 < 10 (Lesson 5.3)