Graph Using a Table of Values f(x)=-3x^2+3

$f (x) = - 3 x^{2} + 3$

Step 1

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

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

Step 2

Simplify $- 3 {(- 2)}^{2} + 3$ .

Simplify each term.

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

$y = - 3 \cdot 4 + 3$

Multiply $- 3$ by $4$ .

$y = - 12 + 3$

Add $- 12$ and $3$ .

$y = - 9$

Step 3

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

$y = - 3 {(- 1)}^{2} + 3$

Step 4

Simplify $- 3 {(- 1)}^{2} + 3$ .

Simplify each term.

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

$y = - 3 \cdot 1 + 3$

Multiply $- 3$ by $1$ .

$y = - 3 + 3$

Add $- 3$ and $3$ .

$y = 0$

Step 5

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

$y = - 3 {(0)}^{2} + 3$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 0^{2} + 3$

Remove parentheses.

$y = - 3 {(0)}^{2} + 3$

Simplify $- 3 {(0)}^{2} + 3$ .

Simplify each term.

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

$y = - 3 \cdot 0 + 3$

Multiply $- 3$ by $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

Step 7

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

$y = - 3 {(1)}^{2} + 3$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 1^{2} + 3$

Remove parentheses.

$y = - 3 {(1)}^{2} + 3$

Simplify $- 3 {(1)}^{2} + 3$ .

Simplify each term.

One to any power is one.

$y = - 3 \cdot 1 + 3$

Multiply $- 3$ by $1$ .

$y = - 3 + 3$

Add $- 3$ and $3$ .

$y = 0$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 2^{2} + 3$

Remove parentheses.

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

Simplify $- 3 {(2)}^{2} + 3$ .

Simplify each term.

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

$y = - 3 \cdot 4 + 3$

Multiply $- 3$ by $4$ .

$y = - 12 + 3$

Add $- 12$ and $3$ .

$y = - 9$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 9 \\ - 1 & 0 \\ 0 & 3 \\ 1 & 0 \\ 2 & - 9 \end{array}$

Step 12

Graph Using a Table of Values f(x)=-3x^2+3

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