Find the Standard Form of the Parabola f(x)=x^2+2x-8

$f (x) = x^{2} + 2 x - 8$

Step 1

Write $f (x) = x^{2} + 2 x - 8$ as an equation.

$y = x^{2} + 2 x - 8$

Step 2

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + 2 x - 8 = y$

Step 3

Add $8$ to both sides of the equation.

$x^{2} + 2 x = y + 8$

Step 4

Complete the square.

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1$

$b = 2$

$c = 0 = y + 8$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = y + 8$

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{2}{2 \cdot 1}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = \frac{2}{2 \cdot 1}$

Rewrite the expression.

$d = 1$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = 0 - \frac{2^{2}}{4 \cdot 1}$

Simplify the right side.

Simplify each term.

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

$e = 0 - \frac{4}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 0 - \frac{4}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$e = 0 - \frac{4}{4}$

Rewrite the expression.

$e = 0 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$e = 0 - 1$

Subtract $1$ from $0$ .

$e = - 1$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form ${(x + 1)}^{2} - 1$ .

${(x + 1)}^{2} - 1 = y + 8$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

${(x + 1)}^{2} = y + 8 + 1$

Add $8$ and $1$ .

${(x + 1)}^{2} = y + 9$

Find the Standard Form of the Parabola f(x)=x^2+2x-8

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