Modeling with Quadratic Functions Answers

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)

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?

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 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?

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?

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

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 image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.