Interpret Structure of Expressions
Create Expressions & Equations
Solve Quadratic Equations
Build Quadratic Functions
Model Quadratic Functions
100
Which expression is equivalent to
121x2 – 64y2 ?
A. (11x – 16y)(11x + 16y)
B. (11x – 16y)(11x – 16y)
C. (11x + 8y)(11x + 8y)
D. (11x + 8y)(11x – 8y)
D. (11x + 8y)(11x – 8y)
100
What are the zeros of the function represented by the quadratic expression 2x2 + x – 3?
x = (–3)/ 2 x and x = 1
100
What are the solutions to the equation 2x2 – 2x – 12 = 0?
A. x = –4, x = 3
B. x = –3, x = 4
C. x = –2, x = 3
D. x = –6, x = 2
C. x = –2, x = 3
100
What explicit expression can be used to find the next term in this sequence?
2, 8, 18, 32, 50, . . .
A. 2n
B. 2n + 6
C. 2n2
D. 2n2 + 1
C. 2n2
100
1. A flying disk is thrown into the air from a height of 25 feet at time t = 0. The function that models this situation is h(t) = –16t2 + 75t + 25, where t is measured in seconds and h is the height in feet. What values of t best describe the times when the disk is flying in the air?
A. 0 < t < 5
B. 0 < t < 25
C. all real numbers
D. all positive integers
A. 0 < t < 5
200
What is a common factor for the expression 24x2 + 16x + 144?
A. 16
B. 8x
C. 3x2 + 2x + 18
D. 8(x – 2)(3x2 + 9)
C. 3x2 + 2x + 18
--------------
factored: 8(3x2 + 2x + 18)
200
What is the vertex of the graph of f(x) = x2 + 10x – 9?
A. (5, 66)
B. (5, –9)
C. (–5, –9)
D. (–5, –34)
D. (–5, –34)
200
What are the solutions to the equation 6x2 – x – 40 = 0 ?
A. x=(–8)/3, x =(–5)/2
B. x=(–8)/3, x =5/2
C. x=5/2, x=8/3
D. x=–5/2, x=8/3
D. x=–5/2, x=8/3
200
The function s(t) = vt + h – 0.5at2 represents the height of an object, s, from the ground after the time, t, when the object is thrown with an initial velocity of v at an initial height of h and where a is the acceleration due to gravity (32 feet per second squared).
A baseball player hits a baseball 4 feet above the ground with an initial velocity of 80 feet per second. About how long will it take the baseball to hit the ground?
A. 2 seconds
B. 3 seconds
C. 4 seconds
D. 5 seconds
D. 5 seconds
200
What is the average rate of change of x over the interval –2 ≤ x ≤ 0?
A. –10
B. –5
C. 5
D. 10
B. –5
300
Which of these shows the complete factorization of 6x2y2 – 9xy – 42?
A. 3(2xy2 – 7)(xy2 + 2)
B. (3xy + 6)(2xy – 7)
C. 3(2xy – 7)(xy + 2)
D. (3xy2 + 6)(2xy2 – 7)
C. 3(2xy – 7)(xy + 2)
300
The expression –x2 + 70x – 600 represents a company’s profit for selling x items. For which number(s) of items sold is the company’s profit equal to $0?
A. 0 items
B. 35 items
C. 10 items and 60 items
D. 20 items and 30 items
C. 10 items and 60 items
300
What are the solutions to the equation x2 – 5x = 14 ?
A. x = –7, x = –2
B. x = –14, x = –1
C. x = –2, x = 7
D. x = –1, x = 14
C. x = –2, x = 7
300
A café’s annual income depends on x, the number of customers. The function I(x) = 4x2 – 20x describes the café’s total annual income. The function C(x) = 2x2 + 5 describes the total amount the café spends in a year. The café’s annual profit, P(x), is the difference between the annual income and the amount spent in a year.
Which function describes P(x)?
A. P(x) = 2x2 – 20x – 5
B. P(x) = 4x3 – 20x2
C. P(x) = 6x2 – 20x + 5
D. P(x) = 8x4 – 40x3 – 20x2 – 100x
A. P(x) = 2x2 – 20x – 5
300
What is the end behavior of the graph of f(x) = –0.25x2 – 2x + 1?
A. As x increases, f(x) increases. As x decreases, f(x) decreases.
B. As x increases, f(x) decreases. As x decreases, f(x) decreases.
C. As x increases, f(x) increases. As x decreases, f(x) increases.
D. As x increases, f(x) decreases. As x decreases, f(x) increases.
B. As x increases, f(x) decreases. As x decreases, f(x) decreases.
400
Factor the expression 16a2 – 81.
(4a + 9)(4a – 9)
400
A garden measuring 8 feet by 12 feet will have a walkway around it. The walkway has a uniform width, and the area covered by the garden and the walkway is 192 square feet. What is the width of the walkway?
A. 2 feet
B. 3.5 feet
C. 4 feet
D. 6 feet
A. 2 feet
400
An object is thrown in the air with an initial velocity of 5 m/s from a height of 9 m. The equation h(t) = –4.9t2 + 5t + 9 models the height of the object in meters after t seconds.
About how many seconds does it take for the object to hit the ground? Round your answer to the nearest tenth of a second.
A. 0.940 second
B. 1.50 seconds
C. 2.00 seconds
D. 9.00 seconds
C. 2.00 seconds
400
Which statement BEST describes the graph of f(x + 6)?
A. The graph of f(x) is shifted up 6 units.
B. The graph of f(x) is shifted left 6 units.
C. The graph of f(x) is shifted right 6 units.
D. The graph of f(x) is shifted down 6 units.
B. The graph of f(x) is shifted left 6 units.
400
Which function is shown in the graph?
A. f(x) = x2 – 3x – 10
B. f(x) = x2 + 3x – 10
C. f(x) = x2 + x – 12
D. f(x) = x2 – 5x – 8
A. f(x) = x2 – 3x – 10
500
Factor the expression 12x2 + 14x – 6.
2(3x – 1)(2x + 3)
500
The formula for the area of a circle is A = πr2.
Which equation shows the formula in terms of r?
A. r = (2A)/π
B. r = (sqrtA)/π
C. r = sqrt(A/π)
D. r = A/(2π)
C. r = sqrt(A/π)
500
Which statement BEST describes how the graph of g(x) = –3x2 compares to the graph of f(x) = x2 ?
A. The graph of g(x) is a vertical stretch of f(x) by a factor of 3.
B. The graph of g(x) is a reflection of f(x) across the x-axis.
C. ?The graph of g(x) is a vertical shrink of f(x) by a factor of 1 /3 and a reflection across the x-axis.
D. ?The graph of g(x) is a vertical stretch of f(x) by a factor of 3 and a reflection across the x-axis.
D. ?The graph of g(x) is a vertical stretch of f(x) by a factor of 3 and a reflection across the x-axis.
500
The function f(t) = –16t2 + 64t + 5 models the height of a ball that was hit into the air, where t is measured in seconds and h is the height in feet. This table represents the height, g(t), of a second ball that was thrown into the air.
Which statement BEST compares the length of time each ball is in the air?
A. ?The ball represented by f(t) is in the air for about 5 seconds, and the ball represented by g(t) is in the air for about 3 seconds.
B. ?The ball represented by f(t) is in the air for about 3 seconds, and the ball represented by g(t) is in the air for about 5 seconds.
C. ?The ball represented by f(t) is in the air for about 3 seconds, and the ball represented by g(t) is in the air for about 4 seconds.
D. ?The ball represented by f(t) is in the air for about 4 seconds, and the ball represented by g(t) is in the air for about 3 seconds.
D. ?The ball represented by f(t) is in the air for about 4 seconds, and the ball represented by g(t) is in the air for about 3 seconds.