Chapter 1.1, Problem 5E

Solution

To complete: The table for values of a function by filling in blank.

The completed table is,

x	-4	-2	0	2	4
y ( x )	8	2	0	2	8

Given data: The function $y=\frac{1}{2}{x}^2$ and the table of values of the function is

x	-4	-2	0	2	4
y ( x )	?	?	?	?	?

Explanation:

The function is $y=\frac{1}{2}{x}^2\text{or}y=0.5x^2$ .

Calculate values of y by substituting respective values of variable x as:

  $\begin{array}{c}y\left(-4\right)=0.5{\left(-4\right)}^2\\ =0.5\cdot 16\\ =8\end{array}$

  $\begin{array}{c}y\left(-2\right)=0.5{\left(-2\right)}^2\\ =0.5\cdot 4\\ =2\end{array}$

  $\begin{array}{c}y\left(0\right)=0.5{\left(0\right)}^2\\ =0.5\cdot 0\\ =0\end{array}$

  $\begin{array}{c}y\left(-2\right)=0.5{\left(2\right)}^2\\ =0.5\cdot 4\\ =2\end{array}$

  $\begin{array}{c}y\left(-4\right)=0.5{\left(-4\right)}^2\\ =0.5\cdot 16\\ =8\end{array}$

The completed table is,

x	-4	-2	0	2	4
y ( x )	8	2	0	2	8