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

$f (x) = - 2 x^{2}$

Step 1

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

$y = - 2 {(- 2)}^{2}$

Step 2

Simplify $- 2 {(- 2)}^{2}$ .

Multiply $- 2$ by ${(- 2)}^{2}$ by adding the exponents.

Multiply $- 2$ by ${(- 2)}^{2}$ .

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

$y = {(- 2)}^{1} {(- 2)}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = {(- 2)}^{1 + 2}$

Add $1$ and $2$ .

$y = {(- 2)}^{3}$

Raise $- 2$ to the power of $3$ .

$y = - 8$

Step 3

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

$y = - 2 {(- 1)}^{2}$

Step 4

Simplify $- 2 {(- 1)}^{2}$ .

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

$y = - 2 \cdot 1$

Multiply $- 2$ by $1$ .

$y = - 2$

Step 5

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

$y = - 2 {(0)}^{2}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - 2 \cdot 0^{2}$

Remove parentheses.

$y = - 2 {(0)}^{2}$

Simplify $- 2 {(0)}^{2}$ .

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

$y = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0$

Step 7

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

$y = - 2 {(1)}^{2}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = - 2 {(1)}^{2}$

Simplify $- 2 {(1)}^{2}$ .

One to any power is one.

$y = - 2 \cdot 1$

Multiply $- 2$ by $1$ .

$y = - 2$

Step 9

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

$y = - 2 {(2)}^{2}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = - 2 \cdot 2^{2}$

Remove parentheses.

$y = - 2 {(2)}^{2}$

Simplify $- 2 {(2)}^{2}$ .

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

$y = - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$y = - 8$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 8 \\ - 1 & - 2 \\ 0 & 0 \\ 1 & - 2 \\ 2 & - 8 \end{array}$

Step 12

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

Related Questions

Support LCMGCF.com by disabling your adblocker.