Quadratic Functions

Question

The height  (in feet) of a ball thrown by a child is ² where   is the horizontal distance in feet from the point at which the ball is thrown.

(a) How high is the ball when it leaves the child's hand?  ____feet

(b) What is the maximum height of the ball? _____  feet

(c) How far from the child does the ball strike the ground?

Answer 1

(a)

y(0) = 3 ft

(b)

The maximum height is at the vertex, where

x = -b/(2a) = -4/[2(-1/12)] = ?

Evaluate y at this value of x to get maximum height.

(c)

Set y=0 and solve the resulting quadratic equation for x using the quadratic formula. You will a negative and a positive solution. Since x starts at zero, the positive solution is the correct one.