MATH UNIT TEST

The graph of f(x) = x2 is translated to form g(x) = (x - 5)2 + 1. Which graph represents g(x)?

(5, 1)

The graph of which function has a y-intercept of 3?

(betwwen -2 and -1, a little under 1 )

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

(−5, 41)

The axis of symmetry for the graph of the function is x=6. What is the value of b?

-3

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is . What is the value of b?

-9

What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x)=(x−4)2+2?

4

The function f(x) = -10(x)(x - 4) represents the approximate height of a projectile launched from the ground into the air as a function of time in seconds, x. How long, from launch to landing, does the projectile stay in the air?

4 seconds

On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time. Time (x) Height (y) 0102241610 How high was the ball after 8 seconds?

42 feet

Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?

6

The height of a hill, h(x), in a painting can be written as a function of x, the distance from the left side of the painting. Both h(x) and x are measured in inches. What is the height of the hill in the painting 3 inches from the left side of the picture?

6 inches

The function f(x) = -(x - 20)(x - 100) represents a company's monthly profit as a function of x, the number of purchase orders received. Which number of purchase orders will generate the greatest profit?

60

liana started to evaluate the function f(x) = 2x2 - 3x + 7 for the input value 2. f(x) = 2(2)2 - 3(2) + 7 = 2(4) - 3(2) + 7

9

The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true?

The function is decreasing for all real values of x wherex < 1.5.

Which is the graph of f(x) = -(x + 3)(x + 1)?

(-2, 1)

What is the midpoint of the x-intercepts off(x) = (x - 2)(x - 4)?

(3, 0)

What is the vertex of g(x) = -3x2 + 18x + 2?

(3, 29)

What is the vertex of g(x) = 8x2 - 64x?

(4, -128)

What is the x-intercept of the graph of the function f(x) = x2 − 16x + 64?

(8, 0)

Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?

(_-4, 2) the U is going downwards

Which is the graph of f(x) = (x - 1)(x + 4)?

(between -2 and -1, 6)

Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options.

* The vertex of the function is (-3, -13). *The graph increases over the interval (-3, ).

Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?

1 to 2.5

The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the radius of the flowerbed in feet. If the vertex of the function is at the point (0, 0.5), what is the recommended amount of mulch for a flowerbed with a radius of 20 feet? Round to the nearest tenth if necessary.

13 cubic yards

Which value is needed in the expression below to create a perfect square trinomial? x2+8x+______

16

The zeros of a parabola are 6 and −5. If (-1, 3) is a point on the graph, which equation can be solved to find the value of a in the equation of the parabola?

3 = a(−1 − 6)(−1 + 5)

A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = -2(x)(x - 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?

30 inches

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -3x2 - 36x - 60?

The graph of f(x) = x2 is made narrower.

The function g(x) = 10x2 - 100x + 213 written in vertex form is g(x) = 10(x - 5)2 - 37. Which statements are true about g(x)? Select three options.

The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up.

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?

The y-intercept will always be the vertex.

Which function has only one x-intercept at (−6, 0)?

f(x) = (x + 6)(x + 6)

Which function in vertex form is equivalent to f(x) = 4 + x2 - 2x?

f(x) = (x - 1)2 + 3

The vertex form of a function is g(x) = (x - 3)2 + 9. How does the graph of g(x) compare to the graph of the functionf(x) = x2?

g(x) is shifted 3 units right and 9 units up

Which values for h and k are used to write the function in vertex form?

h=−6, k=−30

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x + 3)2 + 4?

left 3, up 4

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ?

right 4, down 9

Which graph shows the axis of symmetry for the function f(x) = (x - 2)2 + 1?

vertex 2

What is the axis of symmetry of h(x) = 5x2 + 40x + 64?

x = −4

What are the coordinates of the vertex of the function f(x)=x2+10x−3?

(-5, -28)

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)?

(-6, 0)

Which graph represents a quadratic function with a vertex at (0, 0)?

(0, 0)

What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?

(0, 5)

What is the vertex of g(x) = 3x2 − 12x + 7?

(2, −5)

The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true?

The function is negative for all real values of x where-6 < x < -2.

What is f(x) = 2x2 + 28x - 5 written in vertex form?

f(x) = 2(x + 7)2 - 103

The vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0, −70). The equation of the function in vertex form, f(x)=a(x−h)2+k, is shown. −70=a(0−6)2+2 What is the value of a?

−2

The graph shows the axis of symmetry for a quadratic function f(x). On a coordinate plane, a vertical dashed line at (4, 0) is parallel to the y-axis. Which could be the function?

f(x) = (x - 4)2

Which function has a range of {y|y ≤ 5}?

f(x) = -(x - 4)2 + 5

Which represents a quadratic function?

f(x) = -7x2 - x + 2

The first steps in writing f(x) = 3x2 - 24x + 10 in vertex form are shown. f(x) = 3(x2 - 8x) + 10 = 16 What is the function written in vertex form?

f(x) = 3(x - 4)2 - 38

Which quadratic function is represented by the table?

f(x) = 3x2 - 2x + 5

The graph of which function has an axis of symmetry at x = 3?

f(x) = x2 - 6x - 1

What is the equation of the translated function, g(x), iff(x) = x2?

g(x) = (x + 4)2 + 6

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

left 1 unit

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?

right 2, up 3

Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table. Which equation models the motion of the ball?

y = -16(x - 2)2 + 68