Chapter 9, Problem 23SGR

To determine

To compare: The graph of the given function to the graph of h = $t^2$

Answer to Problem 23SGR

Reflected across the t -axis, vertically stretched and translated up 100 units

Explanation of Solution

Given Information: It is given a ball is dropped off a cliff that is 100 feet high. The function h = -16 $t^2$ +100 models the height h of the ball after t seconds.

The graph of $g(x)=a{(x-h)}^2+k$ is the graph of f(x) translated right h units when h > 0. Left |h| units when h < 0 translated up k units when k > 0, translated down |k| units when k < 0 reflected across the x-axis when a < 0, vertically compressed when 0 < |a| <1

For h = -16 $t^2$ +100, a = -16

And k = 100

Since a = -16 <0

There is a reflection and |a| = |-16| >1, there is a vertical stretched. Since k = 100 > 0, there is a translation up 100 units. The graph of $h=-16t^2+100$ is then the graph of h = $t^2$ reflected across the t -axis, vertically stretched and translated up 100 units.