Modeling with Quadratic Functions Answers

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?

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

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?

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.

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

On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.Time (x) Height (y) 0102241610How high was the ball after 8 seconds?

The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?

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

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?