Modeling with Quadratic Functions Answers

The height of a hill, h(x), in a painting can be written as a function of x, the distance from the left side of the painting. Both h(x) and x are measured in inches.

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?

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 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 inches in depth?

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?

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

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?

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.

The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation. 60=a(0+5)(0+3)

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?

The table shows the approximate height of a projectile x seconds after being fired into the air.