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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Simplify ${(- 2)}^{2} - 2 \cdot - 2 - 3$ .

Simplify each term.

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

$y = 4 - 2 \cdot - 2 - 3$

Multiply $- 2$ by $- 2$ .

$y = 4 + 4 - 3$

Simplify by adding and subtracting.

Add $4$ and $4$ .

$y = 8 - 3$

Subtract $3$ from $8$ .

$y = 5$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

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

$y = 1 - 2 \cdot - 1 - 3$

Multiply $- 2$ by $- 1$ .

$y = 1 + 2 - 3$

Simplify by adding and subtracting.

Add $1$ and $2$ .

$y = 3 - 3$

Subtract $3$ from $3$ .

$y = 0$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

$y = 0 - 2 \cdot 0 - 3$

Multiply $- 2$ by $0$ .

$y = 0 + 0 - 3$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

One to any power is one.

$y = 1 - 2 \cdot 1 - 3$

Multiply $- 2$ by $1$ .

$y = 1 - 2 - 3$

Simplify by subtracting numbers.

Subtract $2$ from $1$ .

$y = - 1 - 3$

Subtract $3$ from $- 1$ .

$y = - 4$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Simplify ${(2)}^{2} - 2 \cdot 2 - 3$ .

Simplify each term.

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

$y = 4 - 2 \cdot 2 - 3$

Multiply $- 2$ by $2$ .

$y = 4 - 4 - 3$

Simplify by subtracting numbers.

Subtract $4$ from $4$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 5 \\ - 1 & 0 \\ 0 & - 3 \\ 1 & - 4 \\ 2 & - 3 \end{array}$

Step 12

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

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