Algebra I: Modeling With Quadratic Functions

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

(-5, -28)

Over which interval is the graph of f(x) = 1/2x2 + 5x + 6 increasing?

(-5, ∞)

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

(-6,0)

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

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

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

(-8, infinity)

Over which interval is the graph of f(x) = -x2 + 3x + 8 increasing?

(-∞, 1.5)

What is the y-intercept of the quadratic function f(x) = (x - 6)(x - 2)?

(0,12)

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

(2, -5)

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

(3, -7)

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

(3, 29)

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

(3,0)

What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

(6, -31)

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 axis of symmetry for the graph of the function f(x)1/4x2+bx+10 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 x=3/2 . What is the value of b?

-9

A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6, 0). The y-intercept of the first parabola is (0, -12). The y-intercept of the second parabola is (0, -24). What is the positive difference between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to the nearest tenth.

0.5

The zeros of a parabola are -4 and 2, and (6, 10) is a point on the graph. Which equation can be solved to determine the value of a in the equation of the parabola?

10 = a(6 + 4)(6 - 2)

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

16

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 whole number.

26 cubic yards

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

3

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)

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

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

49/4

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

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

Graph A

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

Graph A

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

Graph B

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

Graph C

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 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

The graph of the function f(x) = -(x + 3)(x - 1) is shown below. Which statement about the function is true?

The function is negative for all real values of x where x < -3 and where x > 1

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

Which statements about the graph of the function f(x) = -x^2 - 4x + 2 are true? Select three options.

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

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

f(x) = 8 (x+1/4)2-1/2

Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?

f(x) = −6(x + 1)(x + 5)

The graph shows the axis of symmetry for a quadratic function f(x). 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

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

f(x)=x^2-6x-1

What is the equation of the translated function, g(x), if f(x) = x^2?

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

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?

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

The function f(x) = x^2 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-4)^2+9

Which values for h and k are used to write the function f(x)=x2+12x+6 in vertex form?

h=-6, k=-30

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) = x^2 to g(x) = (x + 3)^2 + 4?

left 3, down 4

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

right 2, up 3

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 is one of the transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3?

shifted right 7 units

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

x=-4

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

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)

What is the range of the function f(x) = 3x^2 + 6x - 8?

{y|y ≥ -11}

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, infinity)

Which statements about the graph of the function f(x) = 2x^2 - x - 6 are true? Select two options.

The vertex of the function is (1/4, -6 1/8) . The function has two x-intercepts.

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 graph is negative on the entire interval -4 < x < 6

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

What is the first step in writing f(x) = 6x2 + 5 - 42x in vertex form?

Write the function in standard form

The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function?

all real numbers greater than or equal to -1

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

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

Which function has a vertex at the origin?

f(x) = -x^2