Algebra EOC Flash Cards
When do you use an open circle to graph the inequality on a number line?
< or >
how do you simplify (x^2 y^3)(x^3 y^5)?
Add Exponents x^5 y^8
How do you simplify (x^2 y^3)(x^3 y^-5)
Add exponents, then move negatives to the bottom x^5 y^-2...... x^5/y^2
What is the equation of a line that goes through (2,5) and (-2,3)?
(2,5) and (-2,3) m=y2-y1/x2-x1....3-5//-2-2....-2/-4....1/2 Use y=mx+b to find b 5=1/2(2)+b b=4 y=1/2x+4
What happens to a graph when you multiply a function by a constant? k*f(x)
k*f(x) The graph compresses vertically (0<k<1) or stretches vertically (k>1) It flips if k is a negative (y is negative)
How do you find the slope from a graph?
m= rise/run
What is the slope of any line perpendicular to y=2x+3?
m=-1/2
What is the slope of any line parallel to y=2x+3?
m=2
Write the equation of a line that has a slope of 2 and goes through (3, -4)
m=2 (3,-4) y=mx+b -4=2(3)+b b=-10 y=2x-10
How do you find the slope from two point? (2,3) and (5,-6)
m=y2-y2/x2-x1....-6-3/5-5...-9/3....-3
When do you use a closed circle to graph the inequality on a number line?
≤ or ≥
How do you simplify (x^2 y^3)^0
Anything to the zero power is 1
What is the formula for standard form?
Ax+By=C
How do you graph x≥2 on a number line?
Closed circle at 2. Arrow pointing right
How do we simplify (2x^2+3x-5)+(3x^2-6x-2)?
Combine like terms 5x^2 - 3x - 7
How do you simplify 2x+3+5x-6?
Combine like terms 7x-3
What property is represented by: a+b=b+a?
Commutative Property of Addition
What is the first step to solving 2x/18=x+1/12
Cross multiply. x=3
How do you change point-slope form to slope-intercept? y-2=1/2(x-4)
Distribute 1/2 and add 2 y-2=1/2(x-4) y=1/2x+0 y=1/2x
What are the steps to solving 2(x+5)+3x=4x-10
Distribute 2 to parathesis. Combine like terms. Subtract 4x to both sides. Subtract 10 from both sides. x=-20
How do we simplify (2x^2+3x-5)-(3x^2-6x-2)?
Distribute negative one to all of the 2nd term (2x^2+3x-5)+(-3x^2+6x+2) combine like terms -x^2+9x-3
How do you simplify 2x(2x^2+3x-5)?
Distributive Property 4x^3 + 6x^2 - 10x
How do you simplify 2(3x+5)?
Distributive Property 6x+10
How do you simplify 3(2x-5)+3x
Distributive property. Combine like terms. 9x-15
Solve for w: V=lwh
Divide both sides by lh. w=V/lh
How can you solve the following? 2x-3y=8 -2x+5y=-12
Elimination by adding (1,-2)
How can you solve the following? 4x-6y=16 -2x+5y=-12
Elimination by multiplication first Multiply the bottom equation by 2 (1, -2)
How do you fully factor: 4x^2+12xy+9y^2?
Factor by remembering special case a^2+2ab+b^2=(a+b)^2 (2x+3y)^2
How do you fully factor: 4x^2-9y^2?
Factor by remembering the difference of two squares... a^2-b^2=(a-b)(a+b) (2x-3y)(2x+3y)
How do you solve for the x-intercepts of y=x^2+4x-12
Factor, set each factor = 0 x=-6 and x=2
How do you solve the following equation? 0=x^2+4x+3
Factor, set each factor = 0, solve for x x=-1 and x=-3
When mapping functions if every x-value has only one line coming off of it....is it a function or not?
Function... Every input only have one output
Using the vertical line test on a graph, how can you tell if the graph is a function?
If a vertical line drawn anywhere on the graph only hits the graph ONE time.
Using the vertical line test on a graph how can you tell if the graph is not a function?
If a vertical line drawn anywhere on the graph, hits the graph more than once.
How do you solve the following equation? 0=x^2+6x+3
Quadratic Equation (cannot factor) -0.55 and -5.45 (rounded to the nearest hundredth)
How does the slope of two parallel lines relate?
Same or Equal
How do you solve the following equation? -6 = x^2 + 6x
Set = 0, Quadratic Formula 0=x^2+6x+6 -4.73 and -1.27 (Rounded to the nearest hundredth)
How do you solve the following equations? -5x=x^2 + 6
Set =0, Set each factor =0, solve x=-2 and x=-3
How do we simplify √75 +2√27-√3?
Simplify (take out perfect squares) and combine like terms √75 +2√27-√3 5√3 +2*3√3-√3 10√3
if the slope of a line looks like "|" is it positive, negative, zero, or undefined?
Undefined
How do you simplify: (3x-5)(2x+3)
Use Box Method or FOIL to multiply 6x^2 - x - 15
How do you simplify (3x+4y)^2?
Use Box Method or Foil to multiply (3x + 4y)(3x+4y) 9x^2 +24xy+16y^2
How do you simplify (3x-4y)(3x+4y)
Use Box Method or Foil to multiply 9x^2 - 16y^2
What is the vertex form of a quadratic equation?
Vertex Form y=a(x-h)^2 + k
What is the vertex of y=2(x-6)^2 +3
Vertex y=2(x-6)^2 + 3 is (6,3)
How do you factor fully? x^2+3x-4
What two numbers multiply to be -4 and add to be 3? (x+4)(x-1)
What happens to a graph when you multiply the x by a constant? f(k*x)
f(k*x) The graph stretches horizontally (wide) (0<k<1) The graph compresses horizontally (narrower) (k>1) It flips if k is negative (x is negative)
What happens to a graph when you add a constant to a function? f(x)+k
f(x)+k Shifts graph up if k is positive shifts graph down if k is negative
if f(x)=2x+9 and g(x)=7x-6, when is f(x)=g(x)?
f(x)=g(x) 2x+9=7x-6 x=3
What happens to a graph when you add a constant to the x value? f(x+k)
f(x+k) Shifts the graph to the right if negative Shifts the graph to the left if positive BACKWARDS on the inside!
if h(x)=3x and g(x)=4x-1, when is h(x)=g(x)?
h(x)=g(x) 3x=4x-1 x=1
What is the formula for slope intercept?
y=mx+b
How do you change y=x^2-10x-6 into vertex form?
y=x^2-10x-6 y+6+25=x^2-10x+25 y+31=(x-5)^2 y=(x-5)^2-31 (5,31)
if the slope of a line looks like "-" is it positive, negative, zero, or undefined?
zero
If the slope of a line that looks like "/" positive, negative, zero or undefined?
Positive
C(t)=3t+6 How do you find C(-3)?
Put -3 in all t places and simplify. C(-3)=3(-3)+6....C(-3)=-3
f(x)=-2x+3 How do you find x if f(x)=11?
Put 11 in for f(x) and solve. 11=-2x+3.....x=-4
f(x) = -2x+3 How do you find f(3)?
Put 3 in all x places and simplify. f(3)=-2(3)+3 ... f(3)=-3
How do you graph y=x^2-6x+8?
create a table or find vertex and x or y-intercepts
What values are in the range?
y or output. dependent variable
How do you change the slope-intercept form to Standard Form? y=1/2x-3
Multiply by 2, add 6, subtract 2y y=1/2x-3 x-2y=6
How do you simplify (x^5 y^3)^5
Multiply exponents x^10 y^15
Is the following a function? (2,3), (-2,5), (3,-6), (2,5)
No, 2 repeats
Is the following a function? (2,3), (2,4), (2,5), (2,6)
No, the 2 repeats
When mapping function is one x-value has two or more lines coming off of it...is it a function or not?
Not.... Every input can only have one output.
How do you graph x<2 on a number line?
Open circle at 2. Arrow pointing left
How does the slope for two perpendicular lines relate?
Opposite and Reciprocal
What is the formula for point-slope form?
Point-Slope Form: y-y1 = m(x- x1)
How can you solve the following? y=2x 3x+4y=-11
Substitution 3x+4(2x)=-11 (-1,-2)
How do you change standard form to slope-intercept form? 2x+5y=10
Subtract 2x and divide by 5 2x+5y=10 y=-2/5x+2
How do you solve: 2x+5=5x-10
Subtract 2x from both sides. Add 10 to both sides. Divide by 3 to both sides. x=5
How do you solve -2x+3>11?
Subtract 3 from both sides. Divide by -2 to both sides - flip the inequality symbol since you divided by a negative. x<-4
What are the steps to solving 2x+6=-12
Subtract 6 to both sides. Divide by 2 on both sides. x=-9
How do you simplify (x^5 y^3)/(x^2 y^2)?
Subtract Exponents x^3 y
Solve for x: ax+by=c
Subtract by from both sides. Divide by a to both sides. x=(c-by)/a
How do you fully factor: 2x^2+6x-8?
Take out a GCF first, then what two numbers multiply to be -4 and add to be 3? 2(x+4)(x-1)
How do we simplify √75?
Take out the perfect squares 5√3
How do you find a maximum or minimum for a quadratic function?
The maximum/minimum is the vertex Use the axis of symmetry to find x plug into the equation to find y (x,y)
What will the y-intercept be for the following equation? y=-x^2+6x+2
y-intercept = c = 2
What the two things you should remember about x-intercepts?
Where the line crosses the x-axis and y=0
What are the three things you should remember about the y-intercept?
Where the line crosses the y-axis b value in slope-intercept form x=0
Is the following a function? (2, 4), (-2,5), (3,-6), (-3,-5)
Yes
is the following a function (3,4), (4,2), (5,2), (6,2)
Yes
Will the following graph have a maximum or minimum? y=-x^2+6x+2
a=-1, so the graph will have a maximum
Will the following graph have a parabola that opens up or down? y=-x^2+6x+2
a=-1, so the parabola will open down
Will the following graph have a maximum or minimum? Y=x^2+6x+3
a=1, so the graph will have a minimum
Will the following graph have a parabola that opens up or down? y=x^2+6x+3
a=1, so the parabola will open up
How do you fully factor? 2x^2-x-6?
box method (2x+3)(x-2)
How do you graph y=x^2+4x+3?
create a table or find vertex and x or y-intercepts
If the slope of a line looks like "\" is it positive, negative, zero, or undefined?
negative
How do you solve for the x-intercepts of y=x^2+7x+5?
quadratic formula (cannot factor) -0.81 and -6.19 (Rounded to the nearest hundreth)
What is the x-intercept of y=3x-10?
set y=0 add 10, divide by 3 x=10/3
How do you solve 2x+3>11
subtract 3 to both sides. Divide by 2 to both sides. x>4
What is the quadratic formula?
x = (-b ± √b^2 - 4ac)/2a (will get 2 answers)
What values are in the domain?
x or input. independent variable
What is the axis of symmetry equation?
x= -b/2a
What is another way to write 3<x?
x>3 Flip the inequality symbol when you flip the two sides.
How do you change x^ 5/3 to radical form?
x^ 5/3 = 3√x^5 *the 3 is a little root/index
How do you solve the following equation by completing the square? x^2+8x+5 = 0
x^2+8x+5=0 x^2+8x=-5 x^2+8x+16=-5+16 (x+4)^2=11 x=-4±√11
What will the y-intercept be for the following equation?
y intercept = c = 3