UNIT: QUADRATIC FUNCTIONS ALL THE QUIZES

Which represents a quadratic function? f(x) = −8x3 − 16x2 − 4x f (x) = x 2 + 2x − 5 f(x) = + 1 f(x) = 0x2 − 9x + 7

f (x) = x 2 + 2x − 5

What are the x-intercepts of the graph of the function f(x) = x2 + 4x - 12? (-6, 0), (2,0) (-2, -16), (0, -12) (-6, 0), (-2, -16), (2, 0) (0, -12), (-6, 0), (2, 0)

(-6, 0), (2,0)

The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x - 4) represents the image. At which points does the image cross the x-axis? (-8, 0) and (4, 0) (8, 0) and (-4, 0) (2, 0) and (-1, 0) (-2, 0) and (1, 0)

(-8, 0) and (4, 0)

What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5? (0, -5) (0, -3) (0, 3) (0, 5)

(0, 5)

What is the y-intercept of the quadratic functionf(x) = (x - 8)(x + 3)? (8,0) (0,3) (0,-24) (-5,0)

(0,-24)

What is the y-intercept of the quadratic functionf(x) = (x - 6)(x - 2)? (0,-6) (0,12) (-8,0) (2,0)

(0,12)

What is the vertex of g(x) = 3x2 − 12x + 7? (−6, −5) (−2, −5) (2, −5) (6, −5)

(2, −5)

What is the vertex of g(x) = 8x2 - 48x + 65? (-3, -7) (3, -7) (24, -7) (-24, -7)

(3, -7)

What is the midpoint of the x-intercepts off(x) = (x - 2)(x - 4)? (-3,0) (-1,0) (1,0) (3,0)

(3,0)

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? −6 −2 2 6

-2

The graph of f(x) is shown. Over which interval on the x-axis is there a negative rate of change in the function? -2 to -1 -1.5 to 0.5 0 to 1 0.5 to 1.5

-2 to -1

Which is f(5) for the function -2x2 + 2x - 3? -107 -63 -43 -37

-43

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is . What is the value of b? −18 −9 9 18

-9

Which is f(-3) for the quadratic function graphed? -9 -3 0 9

-9

What is f(−3) for the function f(a)=−2a2−5a+4? −29 −23 1 37

1

The minimum of a parabola is located at (-1, -3). The point (0, 1) is also on the graph. Which equation can be solved to determine the a value in the function representing the parabola? 1 = a(0 + 1)2 - 3 1 = a(0 - 1)2 + 3 0 = a(1 + 1)2 - 3 0 = a(1 - 1)2 + 3

1 = a(0 + 1)2 - 3

Which value is needed in the expression below to create a perfect square trinomial? x2+8x+______ 4 8 16 64

16

How many zero pairs must be added to the functionf(x) = x2 - 10x - 4 in order to begin writing the function in vertex form? 4 10 21 25

25

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far away from the maximum depth is a point on the mirror that is inches in depth? 3 inches 4 inches 5 inches 6 inches

3 inches

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? 14 inches 15 inches 28 inches 30 inches

30 inches

The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation. 60=a(0+5)(0+3) What is the value of a? −7.5 −4 4 7.5

4

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 −2 2 4

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? 0 seconds 1 second 2 seconds 4 seconds

4 seconds

What value for c will make the expression a perfect square trinomial? x2 - 7x + c

49/4

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

6

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 What is the value of the function when x = 2? 9 10 16 17

9

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

A.

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

A.

What is f(x) = 8x2 + 4x written in vertex form? f(x) = 8 - f(x) = 8 - f(x) = 8 - 2 f(x) = 8 - 4

A.

Which graph represents the function f(x) = (x - 5)2 + 3?

A.

Which is the graph of the function f(x) =1/2x2 + 2x - 6?

A.

Which function increases at the fastest rate between x = 0 and x = 8?

B.

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

B.

Sanjay begins to correctly graph the function f(x) = (x + 1)2 - 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay's?

C.

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at -2 and 3. The point (-1, 2) is also on the parabola. Which equation can be used to model the image of the lens? y = (x - 2)(x + 3) y = (x - 2)(x + 3) y = (x + 2)(x - 3) y = (x + 2)(x - 3)

C.

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

C.

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

D.

Which statements about the graph of the function f(x) = 2x2 - x - 6 are true? Select two options. The domain of the function is . The range of the function is all real numbers. The vertex of the function is . The function has two x-intercepts. The function is increasing over the interval (, ∞).

The function has two x-intercepts. The range of the function is all real numbers.

Which statements are true about the graph of the function f(x) = x2 - 8x + 5? Select three options. The function in vertex form is f(x) = (x - 4)2 - 11. The vertex of the function is (-8, 5). The axis of symmetry is x = 5. The y-intercept of the function is (0, 5). The function crosses the x-axis twice.

The function in vertex form is f(x) = (x - 4)2 - 11. The y-intercept of the function is (0, 5). The function crosses the x-axis twice.

The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x wherex < 0. The function is increasing for all real values of x wherex < -1 and where x > 4. The function is decreasing for all real values of x where-1 < x < 4. The function is decreasing for all real values of x wherex < 1.5.

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

The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true? The function is positive for all real values of x wherex > -4. The function is negative for all real values of x where-6 < x < -2. The function is positive for all real values of x wherex < -6 or x > -3. The function is negative for all real values of x wherex < -2.

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

Which statement is true concerning the vertex and the axis of symmetry of g(x)=5x2−10x? The function written in vertex form is g(x)=5(x−1)2−5. The vertex is at (1, -5) and the axis of symmetry is x=1. The vertex is at (1, -5) and the axis of symmetry is y = 1. The vertex is at (0, 0) and the axis of symmetry is x = 1. The vertex is at (0, 0) and the axis of symmetry is y = 1.

The function written in vertex form is g(x)=5(x−1)2−5. The vertex is at (1, -5) and the axis of symmetry is x=1.

Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options. The vertex form of the function is f(x) = (x - 2)2 + 2. The vertex of the function is (-3, -13). The axis of symmetry for the function is x = 3. The graph increases over the interval (-3, ). The function does not cross the x-axis.

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

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 graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.

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

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = -5x2 + 100x - 450? Select three options. The graph of f(x) = x2 is shifted down 50 units. The graph of f(x) = x2 is shifted up 50 units. The graph of f(x) = x2 is shifted left 10 units. The graph of f(x) = x2 is shifted right 10 units. The graph of f(x) = x2 is reflected over the x-axis.

The graph of f(x) = x2 is shifted up 50 units. The graph of f(x) = x2 is shifted right 10 units. The graph of f(x) = x2 is reflected over the x-axis.

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options. The domain is {x|x ≤ -2}. The range is {y|y ≤ 6}. The function is increasing over the interval (-∞ , -2). The function is decreasing over the interval (−4, ∞). The function has a positive y-intercept.

The range is {y|y ≤ 6}. The function is increasing over the interval (-∞ , -2). The function has a positive y-intercept.

The a value of a function in the form f(x) = ax2 + bx + c is negative. Which statement must be true? The vertex is a maximum. The y-intercept is negative. The x-intercepts are negative. The axis of symmetry is to the left of zero.

The vertex is a maximum.

Which statement is true concerning the vertex and axis of symmetry of h(x)=−2x2+8x? The vertex is at (0, 0) and the axis of symmetry is x = 2. The vertex is at (0, 0) and the axis of symmetry is y= 2. The vertex is at (2, 8) and the axis of symmetry is x = 2. The vertex is at (2, 2) and the axis of symmetry is y = 2.

The vertex is at (2, 8) and the axis of symmetry is x = 2.

Part of the graph of the function f(x) = (x + 4)(x - 6) is shown below. Which statements about the function are true? Select two options. The vertex of the function is at (1,-25). The vertex of the function is at (1,-24). The graph is increasing only on the interval −4< x < 6. The graph is positive only on one interval, where x < -4. The graph is negative on the entire interval-4 < x < 6.

The vertex of the function is at (1,-25). The graph is negative on the entire interval-4 < x < 6.

Charla wants to determine the vertex of the function f(x) = x2 - 18x + 60 by changing the function into vertex form. Which statement about the vertex of the function is true? The x-coordinate of the vertex is greater than the y-coordinate. The x-coordinate of the vertex is negative. The y-coordinate of the vertex is greater than the y-intercept. The y-coordinate of the vertex is positive.

The x-coordinate of the vertex is greater than the y-coordinate.

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0? The graph will always have zero x-intercepts. The function will always have a minimum. The y-intercept will always be the vertex. The axis of symmetry will always be positive.

The y-intercept will always be the vertex.

Which function in vertex form is equivalent to f(x) = 4 + x2 - 2x? f(x) = (x - 1)2 + 3 f(x) = (x - 1)2 + 5 f(x) = (x + 1)2 + 3 f(x) = (x + 1)2 + 5

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

The graph shows the axis of symmetry for a quadratic function f(x). Which could be the function? f(x) = (x + 4)2 f(x) = x2 + 4 f(x) = (x - 4)2 f(x) = x2 - 4

f(x) = (x - 4)2

The graph of which function is decreasing over the interval (-4, ∞)? f(x) = (x + 4)2 + 4 f(x) = -(x + 4)2 + 4 f(x) = (x - 4)2 - 4 f(x) = -(x - 4)2 - 4

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

Which represents a quadratic function? f(x) = 2x3 + 2x2 - 4 f(x) = -7x2 - x + 2 f(x) = -3x + 2 f(x) = 0x2 + 3x - 3

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

Which function has a vertex at the origin? f(x) = (x + 4)2 f(x) = x(x - 4) f(x) = (x - 4)(x + 4) f(x) = -x2

f(x) = -x2

What is f(x) = 2x2 + 28x - 5 written in vertex form? f(x) = 2(x + 7)2 - 19 f(x) = 2(x + 7)2 - 103 f(x) = 2(x + 14)2 - 14 f(x) = 2(x + 14)2 - 98

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

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 - 6 f(x) = 3(x + 4)2 - 38 f(x) = 3(x - 4)2 - 6 f(x) = 3(x - 4)2 - 38

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

Which function has two x-intercepts, one at (0, 0) and one at (4, 0)? f(x) = x(x − 4) f(x) = x(x + 4) f(x) = (x − 4)(x − 4) f(x) = (x + 4)(x + 4)

f(x) = x(x − 4)

What is the equation of the translated function, g(x), if f(x) = x2 g(x) = (x - 4)2 + 6 g(x) = (x + 6)2 - 4 g(x) = (x - 6)2 - 4 g(x) = (x + 4)2 + 6

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

The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)? g(x) = (x + 9)2 + 4 g(x) = (x + 9)2 − 4 g(x) = (x − 4)2 + 9 g(x) = (x + 4)2 + 9

g(x) = (x − 4)2 + 9

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = -9(x + 1)2 - 7 g(x) = 4(x - 3)2 + 1 g(x) = -3(x - 4)2 - 6 g(x) = 8(x - 3)2 - 5

g(x) = 8(x - 3)2 - 5

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

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

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? right 1 unit left 1 unit right 2 units left 2 units

left 1 unit

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 right 3, down 4 left 3, down 4 right 3, up 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 ? left 4, down 9 left 4, up 23 right 4, down 9 right 4, up 23

right 4, down 9

What is the axis of symmetry of the function f(x)=−(x+9)(x−21)? x=−15 x=−6 x=6 x=15

x=6

The table shows the approximate height of a projectile x seconds after being fired into the air. Which equation models the height, y, x seconds after firing? y = -10(x)(x - 5) y = 10(x)(x - 5) y = -10(x - 5) y = 10(x - 5)

y = -10(x)(x - 5)

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 = -17(x)(x - 4) y = -16(x)(x - 4) y = -16(x - 2)2 + 68 y = -17(x - 2)2 + 68

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

What is the range of the function f(x) = 3x2 + 6x - 8? {y|y ≥ -1} {y|y ≤ -1} {y|y ≥ -11} {y|y ≤ -11}

{y|y ≥ -11}