trigonomotry 2
Estimate the coordinates of the midpoint of the line segment below:
(-1, 2)
Find the midpoint of the line segment with endpoints (-3,-1) and (1,6).
(-1, 2.5)
Label the point.
(-2, -2)
What are the coordinates of this point?
(-3, 4)
Using the intercept method, what are the two points to plot when graphing the line x + 3y = 6?
(0, 2) and (6, 0)
Which set of ordered pairs is NOT a function?
(1,2) (2,6)(1,5)
Which of the following is an example of an ordered pair?
(2,9)
Based on this graph, what is the solution to the system of equations?
(3, 2)
Solve the system of equations below: y = 3x - 5 y = -2x + 10
(3, 4)
In the equation y = 3|x-4| + 7, what are the coordinates of the vertex?
(4, 7)
Find the midpoint of the line segment with endpoints (6,-2) and (6,4).
(6, 1)
Solve the following system of equations: 2x - 3y = 21 and 5x + 4y = 18
(6,-3)
What are the coordinates of the vertex of the graph y = |x - 9| - 2?
(9, -2)
Factor the following expression: x^2 +9x + 8
(x + 1) (x + 8)
What are the factors of x2 + 7x - 30?
(x + 10)(x - 3)
Complete the square for the following trinomial:
(x-3)2-1
What is the simplified value of the expression below?
-1
Which of the following expressions is a complex number?
-1 + i
Which complex number would look like it was located at the coordinates (-2, 4) if it was graphed?
-2 + 4i
What are the zeros in the following quadratic equation?
-2 and 1/2
What is the slope in this equation? y - 6 = -4(x + 7)
-4
If you don't see a variable listed in a linear system in three variables, you should note that the variable has a coefficient of:
0
What is the x value of the high or low point of the parabola f(x) = x^2 + 1?
0
If the domain of the function f(x) = x^2 is 0 ≤ x, what is the range of f?
0 to infinity
What is the domain of √(x)?
0 to infinity
How many more equations are needed to complete this linear system with three variables?
1
Evaluate |5 - 3| + 4|3 - 5|
10
Find the distance between the two points (4, 1) and (10, 9).
10
A car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots, some that cost $3,000 and some that cost $2,000. If the company is sure that it wants to spend all of its money on 16 new robots, how many of each should it purchase?
12 expensive ones, 4 cheap ones
What number can we substitute for x that will make the absolute value of x = 12?
12, -12
Evaluate h(x) = 5x + 1, when x=3.
16
Evaluate |r+s|-(r+s) when -s = r+8.
16
A quadratic equation will have up to _____ solutions.
2
How many imaginary lines need to be drawn to label points?
2
What is the degree of a quadratic equation?
2
What is the degree of all quadratic functions?
2
What is the slope in this equation? y = 2x - 1
2
An object is dropped from a distance of 64 feet. How long will it take to reach the ground?
2 seconds
Evaluate f(x) = √(x), when x = 9.
3
How many points are recommended for the table method?
3
Our current line has a slope of -1/3. What is the slope of a line that is perpendicular to our line?
3
Which number is represented by the graph below?
3 - 5i
In addition to 1 and 21, what are the factors of 21?
3 and 7
A baseball is thrown from a height of 48 feet off the ground with an initial velocity of 32 feet per second. How many seconds does it take for this baseball to hit the ground?
3 seconds
Which of the following is the greatest common factor of this quadratic? 3x^2 + 3x = 0
3x
Which number is represented by the graph below?
4
Which of the following is an imaginary number?
4/3i
Which of the following is the greatest common factor? 8x^2 + 4x = 0
4x
Find the distance between the two points (-4, -2) and (-4, 3).
5
We have a line with a slope of 5. What is the slope of a line that is parallel to our line?
5
When trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?
5B + 3T = 100
Evaluate |r+4| - 3|s| when r = 5 and s = -1.
6
A parabola that concaves up has y-values that go from 8 to 20. What is the minimum of this parabola?
8
Locate point (-2, 2).
A
Which of the following functions will have the bottom portion of the graph shaded? A: y < x^2 B: y ≤ x^2 C: y > x^2 D: y ≥ x^2
A and B
What type of graph is this?
A parabola
When completing the square, a quadratic trinomial is turned into which one of the following?
A perfect square binomial
A transformation that shifts the graph up/down or left/right is called which one of the following?
A translation
What is the first step to solving the equation |2x + 1| - 5 = 7?
Add 5 to both sides.
Find the breakeven point of the following functions: C(x) = 2x + 1 R(x) = 3x
Approximately (1,3)
Find the breakeven point of the following functions: C(x)= 4x +4 R(x) = 6x
Approximately (2, 12)
Find the breakeven point of the following functions: C(x) = 5x - 7 R(x) = 2x
Approximately (2.33, 4.66)
Find the market equilibrium point (x, y) of the following functions: Supply: y = -0.05x +3.7 Demand: y = 0.02x + 2.3
Approximately (20, 2.7)
Find the market equilibrium point for the following equations: Supply: .10x + 5 Demand: -.15x + 10
Approximately (20, 7)
What type of discontinuity is in the graph of f(x) = 1/(x+2)?
Asymptotic
Which one of the following divides the parabola into two equal halves?
Axis of symmetry
In marketing, the _____ represents the point where products neither make a profit nor incur a loss.
Breakeven Point
Which of the following will work?
Combining the first and second equations to get rid of y.
Which phrase describes a parabola that looks like an upside down U?
Concave down
The _____ is the linear function which represents the seller's cost of a product.
Cost Function
What information is needed for this quadratic function model? A: initial velocity B: initial height C: meters or feet D: time E: A, B, and C
E
What does the zero product property tell us?
If we get a product of zero, at least one of the factors must have been zero.
The point (1, -5) would be found where on the Cartesian plane?
In the lower-right quadrant
How many solutions does this system have?
Infinite
Which of the following is TRUE about the vertex of a parabola?
It is the point where the parabola reaches the maximum or minimum depending on whether it opens down or up
Jonathan enjoys gardening. The east side of his house is 45 units in length. He can put 30 flowers along the length of the east side of his house. Each flower is 1.5 units in length. Assuming that the west side of his house is the same length as the east side, how many flowers can he put along wall B?
Jonathan can put 12 flowers along wall B.
What type of discontinuity is in the graph of f(x) = {x for x<-1; x+1 for x>=-1}?
Jump
Which Law states that the quantity demanded will increase as the price of the product decreases?
Law of Demand
You have 100 feet of fencing. What are the dimensions of the largest rectangular yard you can make with that amount of fencing?
Length of 25 and width of 25
Choose the answer that best describes the function of this graph.Look at the graph that is shown below. Which answer choice best describes the function of this graph?
Negative, Odd
Choose the answer that best describes the function of this graph.
Negative, Odd, Fractional
Solve the equation: -2|x| = 10.
No solution
Solve the equation: |x + 8| = -1.
No solution
How many solutions does this system have?
None
If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?
None
What type of discontinuity is in the graph of f(x) = {2 for x < 0; x+2 for x >= 0}?
None
Factor x^2 + 10x + 12.
None of the answers are correct; this equation cannot be factored further.
Which of the following makes an equation a relation rather than a function?
One input has multiple outputs
What is the special name for the coordinate (0,0)?
Origin
Absolute value symbols should be treated like which one of the following?
Parentheses
What type of discontinuity is in the graph of f(x) = {x for x<3; 0 for x=3; and x for x>3}?
Point
Choose the answer that best describes the function of this graph.Select the best answer choice that describes the function of this graph.
Positive, Fractional
Which scenario best fits the linear equation? y=-2x + 5
Sammy's restaurant started selling chocolate cake as one of the desserts on the menu. Before selling the cake, Sammy starts with a $5 profit. Now, he is losing $2 for each piece of cake he sells.
For the gravity equation, how do you find the time it takes for an object to hit the ground after it's been thrown?
Set f(t) = 0 for the height of the ground.
Which scenario is the best fit for the linear equation? y=200x +1200
Seth buys a limited edition comic book for $1,200. For each year he keeps it in mint condition, the value of the comic book will increase by $200.
The following equation is written in which parabolic form? y = 2x2 - 3x + 12
Standard
What part is shaded for the graph of y < x^2 - 1?
The area outside of the parabola
Which part of the graph is shaded for the quadratic inequality y < x^2 - 4x + 5?
The bottom
The amount of money you spend on coffees every month can be calculated as a function of the number of drinks you order every month. What are the independent and dependent variables in this function?
The independent variable is the number of drinks you order per month and the dependent variable is the amount of money you spend on coffee per month.
Which part of this graph is the solution region?
The overlapping red and green area
Which of the following is not an example of a quadratic equation in real life?
The path of a boat
What does this quadratic function model?
The path of a falling object over time.
For optimization problems, to find the largest area, what point do you look for in the quadratic function?
The vertex point
Which of the following is a solution to the system of equations shown in the graph below?
There is no solution.
If a question requires us to know the value of |2x + y|, but all we know is that |x + y| = 5, what can we do?
There is nothing we can do with the equation.
Which statement is true about the inequality below?
This is not a quadratic inequality.
What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?
Two asymptotic discontinuities
The following equation is written in which parabolic form? y = -(x - 3)2 - 1
Vertex
Completing the square involves changing a quadratic equation from standard form into which one of the following?
Vertex form
When solving a quadratic equation, under what circumstances would the result be two answers that are imaginary numbers?
When the discriminant is negative
Elizabeth found a picture frame on sale. She wants to know if her poster will fit inside the frame, but she left the poster at home. In the image, the blue rectangle represents the frame (perimeter = 43) and the purple rectangle represents the poster. Find x and determine if the poster will fit in the frame.
Yes, the poster will fit in the frame. x = 2.5
The distance formula is a condensed version of:
a2 + b2 = c2
The set of all of the x values of a function, is called the _____.
domain
The points on either end of a line segment are called _____.
endpoints
What is the quadratic modeling function for a marble that is thrown up into the air with an upwards velocity of 10 meters per second from a height of 2 meters?
f(t) = -4.9t^2 + 10t + 2
Which of the following is an example of a power function?
f(x) = 3x^2
Which equation matches the following graph?
f(x)= sqrt (-2x +5)
Which equation matches the following graph?
f(x)= sqrt (x - 2)
Which equation matches the following graph?
f(x)= sqrt (x^2 + 4)
Which one of these functions has a domain of all real numbers?
f(x)=6X/7
Which of the following is written in function notation?
f(x)=x2+2x-1
Given the function below, evaluate g(7).
g(7)=13
If the market price of a product is above the equilibrium price, the quantity supplied is _____ the quantity demanded.
greater than
What inequality symbol is represented by the red dashed line?
greater than
What kind of inequality is used when the line is solid and the shading is above the line?
greater than or equal to
For this equation, what is the slope? y = mx + b
m
The y-coordinate of the vertex of a parabola that opens down is called the _____.
maximum value
Given the following equation, y = 3(x + 5)(x + 9), x = 5 & x = 9 are _____.
not the x-intercepts
Find the distance between the points (-3, 4) and (2, 5).
root 26
In math, i equals _____.
root of -1
All radical functions contain a(n) _____.
square root
Which graph below is a function?
squigly horizontal line
Supply function is defined as _____.
the price and quantity at which the seller is willing to supply the product
For which of the following trinomials can completing the square be done without having to do any extra work on it?
x 2+8x+16
What is the equation of the axis of symmetry of the parabola given by the equation y = 6(x + 1)(x - 5)?
x = 2
The following factors correspond to which one of the following equations: (x + 1) (x - 6)?
x^2 - 5x - 6
Which of the following functions will have a dashed line for the graph?
y < 4x^2 + 1
Which absolute value equation would have a graph that is an upside down V?
y = -2|x-1| + 3
Which one of the following equations is in intercept form?
y = 2 (x - 2) (x + 2)
All of the sides of the square are the same length. Use this information to solve for y.
y = 3
Which of the following is not a quadratic function?
y = 6x^2 + 5x^3 + 8
All of the following are quadratic inequalities, EXCEPT:
y = x^2 + 1
Which of the following equations will be the graph of a parabola?
y = x^2 - 2x + 3
What symbol is used to notate a system of functions?
{
Which equation represents a valid first step to solving the following system of equations using the elimination method if our next step is to add the equations together to eliminate the x variable? 2x - 2y = 5 and -4x + 5y = 11
2(2x - 2y) = 2(5)
Which of the following represents a valid first step to solving this system of equations using the substitution method? 2x - y = 7 x = 2y - 1
2(2y - 1)- y = 7
How many variables does a linear system in three variables have?
3
If a linear system has three variables, how many equations are needed to complete the system?
3
Evaluate |4 + 7| - |4 - 7|
8
What kind of shape do quadratic graphs always follow?
A curve
Which criteria is required for a problem to be a quadratic inequality?
A quadratic must remain after all terms have been moved to one side of the equation.
A graph of y = (1/3)|x| would exhibit which of the following characteristics.
A wide dilation
The length and steepness of a line that shows the rate of change between two values is called the _____.
Slope
What is the first step in the substitution method?
Solving one of the equations for one of the variables.
What is the first step to solving the equation |4x - 2| = 5?
Split the equation into two separate equations.
Which method can be used to solve any system of linear equations in two variables?
Substitution
If a question requires us to know the value of y-x, but all we know is that x+2=y, what can we do?
Subtract x from both sides of the equation.
Consider the following two car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals charges 25 cents per mile with no upfront fee. If TC represent the total cost for the car, and n represents the number of miles, which of the following systems of equations best represents this situation?
TC = 100 + 0.10n TC = 0.25n
Savanna needs to pick up gift bags for a party. She wants gift bags of different shapes, but they must be the same perimeter. She found a bag that is a pink rectangle with a perimeter of 16. Which of the following shapes have the same perimeter as the pink rectangle?
The purple square and the yellow triangle have the same perimeter.
The y-coordinate of the vertex of a parabola that opens up is called the _____.
minimum value
Absolute values make positive numbers _____ and negative numbers _____.
positive, positive
Solve the following inequality.
x < -4 or x > -3
Solve this inequality.
x < -9 or x > -1
Please solve. x^2 + 6x = 0
x = 0 and x = -6
Please solve. 5x^2 - 10x = 0
x = 0 and x = 2
Please solve. x^2 - 4x = 0
x = 0 and x = 4
Solve the equation: |3x - 9| = 27.
x = 12, -6
Solve for x using the image as a reference. The perimeter of the triangle is 36 units.
x = 2
Solve this system. 4x + y = 12 x + y = 6
x = 2 and y = 4
Solve this system. x + y = 6 y = 2x
x = 2 and y = 4
Solve the equation: |2x + 5| = 11.
x = 3 or x = -8
Solve the equation: |2x - 5| = 5.
x = 5 or x = 0
Solve the equation: 3|x - 2| - 1 = 11.
x = 6 or -2
Solve. x - y = 6 x + y = 10
x = 8 and y = 2.
Solve the equation: |x| = 99.
x = 99 or x =-99
What are the most common letters we will see for our variables?
x, y, and z
Solve this system.
x=1, y = 2, z = 3
Find the minimum value of the parabola using the following equation: f(x)=1/4(x+4)^2 +3
y = 3
Find the maximum value of the parabola using the following equation: f(x)=-x^2+4x+3
y = 7
Which of the following is not a quadratic equation?
y = x
What is the correct equation for the following scenario? Alex wants to figure out how much money she will make at the end of the week. She is making $12.50 an hour plus a $20 bonus.
y=12.5x + 20
What is the best equation for the following scenario? A mountain climber starts at the bottom of a mountain and climbs at a rate of 20 feet per hour. What equation represents his rate of climbing?
y=20x
Which symbol is used to represent absolute value?
| |
What is correct expression for the absolute value of the following number: 8?
|8|