Chapter ISG, Problem 9.2.8P

To determine

To graph the given function $y=-\frac{1}{4}{\left(x\right)}^2$ and $h\left(x\right)=-\frac{1}{4}{\left(x-1\right)}^2+4$

Answer to Problem 9.2.8P

The graph shifts 1 units horizontally to the right and 4 units vertically upward from original position.

Explanation of Solution

Given Information: $y=-\frac{1}{4}{\left(x\right)}^2$ and $h\left(x\right)=-\frac{1}{4}{\left(x-1\right)}^2+4$

Formula Used: Graphing Utility

Calculation:

For such equations, a graphing utility can often be used to investigate possible solutions. When a graphing utility is used to solve an equation, usually approximate solutions are obtained.

• $y=-\frac{1}{4}{\left(x\right)}^2$

Put the value of $x$ in $h\left(x\right)$ , get:

$x$	-2	-1	0	1	2
$y$	-1	-0.25	0	-0.25	-1

• $h\left(x\right)=-\frac{1}{4}{\left(x-1\right)}^2+4$

Put the value of $x$ in $h\left(x\right)$ , get:

$x$	-1	0	1	2	3
$h\left(x\right)$	-3	3.75	4	3.75	3

  

The graph shifts 1 units horizontally to the right and 4 units vertically upward from original position.