Graph Using a Table of Values y=x^2+4x+3

$y = x^{2} + 4 x + 3$

Step 1

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

$y = {(- 2)}^{2} + 4 (- 2) + 3$

Step 2

Simplify ${(- 2)}^{2} + 4 (- 2) + 3$ .

Simplify each term.

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

$y = 4 + 4 (- 2) + 3$

Multiply $4$ by $- 2$ .

$y = 4 - 8 + 3$

Simplify by adding and subtracting.

Subtract $8$ from $4$ .

$y = - 4 + 3$

Add $- 4$ and $3$ .

$y = - 1$

Step 3

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

$y = {(- 1)}^{2} + 4 (- 1) + 3$

Step 4

Simplify ${(- 1)}^{2} + 4 (- 1) + 3$ .

Simplify each term.

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

$y = 1 + 4 (- 1) + 3$

Multiply $4$ by $- 1$ .

$y = 1 - 4 + 3$

Simplify by adding and subtracting.

Subtract $4$ from $1$ .

$y = - 3 + 3$

Add $- 3$ and $3$ .

$y = 0$

Step 5

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

$y = {(0)}^{2} + 4 (0) + 3$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = 0^{2} + 4 (0) + 3$

Remove parentheses.

$y = {(0)}^{2} + 4 (0) + 3$

Simplify ${(0)}^{2} + 4 (0) + 3$ .

Simplify each term.

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

$y = 0 + 4 (0) + 3$

Multiply $4$ by $0$ .

$y = 0 + 0 + 3$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

Step 7

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

$y = {(1)}^{2} + 4 (1) + 3$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = 1^{2} + 4 (1) + 3$

Remove parentheses.

$y = {(1)}^{2} + 4 (1) + 3$

Simplify ${(1)}^{2} + 4 (1) + 3$ .

Simplify each term.

One to any power is one.

$y = 1 + 4 (1) + 3$

Multiply $4$ by $1$ .

$y = 1 + 4 + 3$

Simplify by adding numbers.

Add $1$ and $4$ .

$y = 5 + 3$

Add $5$ and $3$ .

$y = 8$

Step 9

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

$y = {(2)}^{2} + 4 (2) + 3$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = 2^{2} + 4 (2) + 3$

Remove parentheses.

$y = {(2)}^{2} + 4 (2) + 3$

Simplify ${(2)}^{2} + 4 (2) + 3$ .

Simplify each term.

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

$y = 4 + 4 (2) + 3$

Multiply $4$ by $2$ .

$y = 4 + 8 + 3$

Simplify by adding numbers.

Add $4$ and $8$ .

$y = 12 + 3$

Add $12$ and $3$ .

$y = 15$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 1 \\ - 1 & 0 \\ 0 & 3 \\ 1 & 8 \\ 2 & 15 \end{array}$

Step 12

Graph Using a Table of Values y=x^2+4x+3

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