Modeling with Quadratic Functions

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

112

121

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

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)

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.The value of f(–10) = 82The graph of the function is a parabola.The graph of the function opens down.The graph contains the point (20, –8).The graph contains the point (0, 0).

The value of f(–10) = 82

The graph of the function is a parabola.

The graph of the function opens down.

The graph contains the point (20, –8).

The graph contains the point (0, 0).

Which equation, when graphed, has x-intercepts at (8, 0) and (−2, 0) and a y-intercept at (0, −48)?

f(x) = −3(x − 8)(x + 2)

f(x) = −3(x + 8)(x − 2)

f(x) = 3(x − 8)(x + 2)

f(x) = 3(x + 8)(x − 2)

three

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 function is decreasing from (−∞, 6.75).

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

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?

11.7 meters

13.8 meters

15.5 meters

17.5 meters

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

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

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

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

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

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

The curve produced by the water coming from a fountain is sketched on the graph.

f(x) = (x – 2)2 + 3

f(x) = –(x – 2)2 + 3

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

f(x) = –(x + 2)2 + 3

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

Option

Jan'ai was asked to determine the minimum for a function with zeros located at –1 and 5, which also has a y-intercept of (0, –25). Her work is shown.Which best describes the first error in Jan'ai's work?

She incorrectly determined the factors for the beginning function.

She incorrectly determined the a value.

She incorrectly transformed the equation to standard form.

She incorrectly determined the x-coordinate of the vertex.

Given the function f(x) = −2x2 + 4x − 7, find f(−4).

−55

−7

All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.

f(x) = –4(x – 50)(x – 250)

f(x) = (x – 50)(x – 250)

f(x) = 28(x + 50)(x + 250)

f(x) = (x + 50)(x + 250)

Giselle graphs the function f(x) = x2. Robin graphs the function g(x) = –x2. How does Robin’s graph relate to Giselle’s?

Robin’s graph is a reflection of Giselle’s graph over the x-axis.

Robin’s graph is a reflection of Giselle’s graph over the y-axis.

Robin’s graph is a translation of Giselle’s graph 1 unit down.

Robin’s graph is a translation of Giselle’s graph 1 unit left.

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

x = −5

x = −3

x = 3

x = 5

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

On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.7, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.5, negative 2.75), (3, negative 2), (6, 4).