Modeling With Quadratic Functions (quiz)

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)

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 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

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)

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 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 image of a parabolic mirror is sketched on a graph. The image can be represented using the function y =-1/8x^2 + 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 7/8 inches in depth?

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?

30 inches

Ja'Von kicks a soccer ball into the air. The function f(x) = -16(x - 2)^2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. What is the maximum height the ball reaches?

64 feet

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground?

50 meters