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 $2$ .

$y = - 1 \cdot 4 + 4 (- 2) - 3$

Multiply $- 1$ by $4$ .

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

Multiply $4$ by $- 2$ .

$y = - 4 - 8 - 3$

Simplify by subtracting numbers.

Subtract $8$ from $- 4$ .

$y = - 12 - 3$

Subtract $3$ from $- 12$ .

$y = - 15$

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.

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{2}$ .

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

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

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

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

Add $1$ and $2$ .

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

Raise $- 1$ to the power of $3$ .

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

Multiply $4$ by $- 1$ .

$y = - 1 - 4 - 3$

Simplify by subtracting numbers.

Subtract $4$ from $- 1$ .

$y = - 5 - 3$

Subtract $3$ from $- 5$ .

$y = - 8$

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 $- 1$ by $0$ .

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

Multiply $4$ 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 $y$ .

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

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.

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

Multiply $- 1$ by $1$ .

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

Multiply $4$ by $1$ .

$y = - 1 + 4 - 3$

Simplify by adding and subtracting.

Add $- 1$ and $4$ .

$y = 3 - 3$

Subtract $3$ from $3$ .

$y = 0$

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 $2$ .

$y = - 1 \cdot 4 + 4 (2) - 3$

Multiply $- 1$ by $4$ .

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

Multiply $4$ by $2$ .

$y = - 4 + 8 - 3$

Simplify by adding and subtracting.

Add $- 4$ and $8$ .

$y = 4 - 3$

Subtract $3$ from $4$ .

$y = 1$

Step 11

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

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

Step 12

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

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