Graph Using a Table of Values f(x)=1/2x^2

$f (x) = \frac{1}{2} x^{2}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot {(- 2)}^{2}$

Step 2

Simplify $\frac{1}{2} \cdot {(- 2)}^{2}$ .

Raise $- 2$ to the power of $2$ .

$y = \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$y = 2$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot {(- 1)}^{2}$

Step 4

Simplify $\frac{1}{2} \cdot {(- 1)}^{2}$ .

Raise $- 1$ to the power of $2$ .

$y = \frac{1}{2} \cdot 1$

Multiply $\frac{1}{2}$ by $1$ .

$y = \frac{1}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot {(0)}^{2}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{1}{2} \cdot 0^{2}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(0)}^{2}$

Simplify $\frac{1}{2} \cdot {(0)}^{2}$ .

Raising $0$ to any positive power yields $0$ .

$y = \frac{1}{2} \cdot 0$

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot {(1)}^{2}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{1}{2} \cdot 1^{2}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(1)}^{2}$

Simplify $\frac{1}{2} \cdot {(1)}^{2}$ .

One to any power is one.

$y = \frac{1}{2} \cdot 1$

Multiply $\frac{1}{2}$ by $1$ .

$y = \frac{1}{2}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot {(2)}^{2}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{1}{2} \cdot 2^{2}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(2)}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of ${(2)}^{2}$ .

$y = \frac{1}{2} \cdot (2 \cdot 2)$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$y = 2$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 2 \\ - 1 & \frac{1}{2} \\ 0 & 0 \\ 1 & \frac{1}{2} \\ 2 & 2 \end{array}$

Step 12

Graph Using a Table of Values f(x)=1/2x^2

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