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 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

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