Quadratic Functions Unit Test

The function f(x) = x2 + 10x - 3 written in vertex form is f(x) = (x + 5)2 - 28. What are the coordinates of the vertex? (-5, -28) (-5, 28) (5, -28) (5, 28)

(-5, -28)

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)

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)? (0,6) (0,-6) (6,0) (-6,0)

(-6,0)

Over what interval is the graph of f(x) = -(x + 8)2 - 1 decreasing?

(-8, ∞)

Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (-∞, -3) (-∞, 2) (-3, ∞) (2, ∞)

(-∞, -3)

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

(0,-24)

The function g(x) = 3x2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)? (−6, −5) (−2, −5) (2, −5) (6, −5)

(2, −5)

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

(3,0)

What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36? (−4, 0) and (9, 0) (4, 0) and (−9, 0) (−3, 0) and (12, 0) (3, 0) and (−12, 0)

(4, 0) and (−9, 0)

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph? (−9, −2) (−17, −2) (−2, −17) (−2, −9)

(−2, −9)

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) (−5, 56) (−5, 76) (−5, 91)

(−5, 41)

The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b?

-3

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c - 4c2 - 3c + 4 -4c2 + 4c + 6 -7c2 + 10c + 6 -4c2 + 4c + 8 -7c2 + 7c + 6

-4c2 + 4c + 6

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

-9

How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial?

1

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

1

Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?

16

What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x + 5)2 + 3?

3

Which zero pair could be added to the function so that the function can be written in vertex form? 3, -3 6, -6 9, -9 36, -36

36, -36

What is the y-value of the vertex of the function f(x) = -(x - 3)(x + 11)? The y-value of the vertex is

49

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

49/4

Consider the quadratic function f(y) = 8y2 - 7y + 6. What is the constant of the function?

6

What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)? The axis of symmetry is x =

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 parent function of the function g(x) = (x - h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, -8). What are the values of h and k? g(x) = (x - )^2 +

9 -8

The graph of f(x) = x2 is translated to form g(x) = (x - 2)2 - 3. 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

1 2 3 5 6 8 9 10 Mary throws a plastic disc to her friend, which her friend catches six seconds after Mary throws it. The table shows the height of the disc at one-second intervals. Assuming that the throw represents projectile motion, what are the missing values in the table? A = 5, B = 3 A = 4, B = 0 A = 4, B = 3 A = 5, B = 0

A = 4, B = 3

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

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

C

Which is the graph of f(x) = x2 - 2x + 3?

NOT C, C IS INCORRECT

What is the equation of the translated function? f(x) = (x - 1)2 - 5 f(x) = (x + 1)2 + 5 f(x) = (x - 5)2 - 1 f(x) = (x + 5)2 + 1

f(x) = (x + 1)2 + 5

Which function in vertex form is equivalent to f(x) = x2 + 6x + 3? f(x) = (x + 3)2 + 3 f(x) = (x + 3)2 − 6 f(x) = (x + 6)2 + 3 f(x) = (x + 6)2 − 6

f(x) = (x + 3)2 − 6

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

Which function has a vertex on the y-axis? f(x) = (x - 2)2 f(x) = x(x + 2) f(x) = (x - 2)(x + 2) f(x) = (x + 1)(x - 2)

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

Which function could be represented by the graph on the coordinate plane? f(x) = (x - 8)2 + 6 f(x) = (x + 8)2 + 6 f(x) = (x + 8)2 - 6 f(x) = (x - 8)2 - 6

f(x) = (x - 8)2 - 6

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

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

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

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

Which quadratic function has a leading coefficient of 2 and a constant term of -3? f(x) = 2x3 - 3 f(x) = -3x2 - 3x + 2 f(x) = -3x3 + 2 f(x) = 2x2 + 3x - 3

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

Which quadratic function is represented by the table? f(x) = 3x2 + 2x - 5 f(x) = 3x2 - 2x + 5 f(x) = 2x2 + 3x - 5 f(x) = 2x2 - 2x + 5

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

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

d

Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply. The domain is all real numbers. The range is all real numbers greater than or equal to 1. The y-intercept is 3. The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2. The graph has two x-intercepts.

The domain is all real numbers. The y-intercept is 3.

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 where x < 0. The function is increasing for all real values of x where x < -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 where x < 1.5.

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

The graph of the function f(x) = -(x + 6)(x + 2) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < -4. The function is increasing for all real values of x where -6 < x < -2. The function is decreasing for all real values of x where x < -6 and where x > -2. The function is decreasing for all real values of x where x < -4.

The function is increasing for all real values of x where x < -4.

The function g(x) = -3x2 - 36x - 60 written in vertex form is g(x) = -3(x + 6)2 + 48. 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.

The function g(x) = -x2 + 16x - 44 written in vertex form is g(x) = -(x - 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -x2 + 16x - 44? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 8 units. The graph of f(x) = x2 is shifted down 44 units. The graph of f(x) = x2 is reflected over the x-axis.

The graph of f(x) = x2 is reflected over t

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 3 units. The graph of f(x) = x2 is shifted up 30 units. The graph of f(x) = x2 is reflected over the x-axis.

The graph of f(x) = x2 is shifted left 3 units.

Gerald graphs the function f(x) = (x - 3)2 - 1. Which statements are true about the graph? Check all that apply. The domain is {x| x ≥ 3}. The range is {y| y ≥ -1}. The function decreases over the interval (-∞, 3). The function increases over the interval (-1, ∞). The axis of symmetry is x = -1. The vertex is (3, -1).

The range is {y| y ≥ -1}. The function decreases over the interval (-∞, 3). The vertex is (3, -1).

The function h(x) = -2x2 + 8x written in vertex form is h(x) = -2(x - 2)2 + 8. The function h(x) is shown on the graph along with the parent function, f(x) = x2. Which statement is true concerning the vertex and axis of symmetry of h(x)? 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.

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = . The domain is all real numbers. The range is all real numbers. The x-intercepts are at (−2, 0) and (1,0). The function is decreasing from (−∞, 6.75).

The vertex is the maximum value. The axis of symmetry is x = . The domain is all real numbers. The x-intercepts are at (−2, 0) and (1,0).

What is true about the function h(x) = x2 + 20x - 17? Check all that apply. The vertex of h is (-10, -117). The vertex form of the function is h(x) = (x + 20)2 - 17. The maximum value of the function is -17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units. The axis of symmetry of function h is x = 20.

The vertex of h is: (-10, -117). To graph the function h, shift the graph of f(x) = x² left 10 units and down 117 units.

Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Check all that apply. 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 vertex of the function is (-3, -13). The graph increases over the interval (-3, ).

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)? Check all that apply. The axis of symmetry is the line x = -5. The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up. The value of a, when the equation is written in vertex form, is negative.

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

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.

f(x)=a(x-h)^2+k

Vertex of a quadratic function (formula)

The graph of the function f(x) = (x + 2)(x − 4) is shown. Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0

all real values of x where 1 < x < 4

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown. Write the function in standard form. f(x) = 5x2 + 40x Factor a out of the first two terms. f(x) = 5(x2 + 8x) Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) - 5(16) What is the function written in vertex form? f(x) = 5(x + 4) - 80 f(x) = 5(x + 8) - 80 f(x) = 5(x + 4)2 - 80 f(x) = 5(x + 8)2 - 80

f(x) = 5(x + 4)2 - 80

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)

Which function has a vertex on the y-axis? f(x) = (x - 2)2 f(x) = x(x + 2) f(x) = (x - 2)(x + 2) f(x) = (x + 1)(x - 2)

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

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x) = (x − 7)2 − 3 g(x) = (x + 7)2 − 3 g(x) = (x − 3)2 − 7 g(x) = (x − 3)2 + 7

g(x) = (x + 7)2 − 3

The function g(x) is a translation of f(x) = (x + 3)2 - 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)? g(x) = (x - 2)2 + k g(x) = (x + 8)2 + k g(x) = (x - h)2 - 5 g(x) = (x - h)2 - 15

g(x) = (x - 2)2 + k

What is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x + 5)2 + 2 g(x) = (x + 2)2 + 5 g(x) = (x - 2)2 + 5 g(x) = (x - 5)2 + 2

g(x) = (x - 5)2 + 2

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = -9(x2 + 2x + 1) - 7 g(x) = 4(x2 - 6x + 9) + 1 g(x) = -3(x2 - 8x + 16) - 6 g(x) = 8(x2 - 6x + 9) - 5

g(x) = 8(x2 - 6x + 9) - 5

Justine graphs the function f(x) = (x - 7)2 - 1. On the same grid, she graphs the function g(x) = (x + 6)2 - 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units

left 13 units, down 2 units

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

Which best describes the transformation from the graph of f(x) = x2 to the graph of f(x) = (x - 3)2 - 1? left 3 units, down 1 unit left 3 units, up 1 unit right 3 units, down 1 unit right 3 units, up 1 unit

right 3 units, down 1 unit

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit

right 3 units, down 3 units

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

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 - 10x +2? right 5, down 23 left 5, down 23 right 5, up 27 left 5, up 27

right 5, down 23

What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)2 + 4?

x = 2 Vertex: (2, 4)

What is the axis of symmetry of h(x) = 6x2 − 60x + 147? x = −5 x = −3 x = 3 x = 5

x = 5

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)? The y-value of the vertex is

y = 121