Find the Standard Form of the Parabola y=x^2+8x+15

$y = x^{2} + 8 x + 15$

Step 1

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

$x^{2} + 8 x + 15 = y$

Step 2

Subtract $15$ from both sides of the equation.

$x^{2} + 8 x = y - 15$

Step 3

Complete the square.

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

$a = 1$

$b = 8$

$c = 0 = y - 15$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = y - 15$

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

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

$d = \frac{8}{2 \cdot 1}$

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

$d = \frac{2 \cdot 4}{2 \cdot 1}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot 4}{2 (1)}$

Cancel the common factor.

$d = \frac{2 \cdot 4}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{4}{1}$

Divide $4$ by $1$ .

$d = 4$

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 $e = c - \frac{b^{2}}{4 a}$ .

$e = 0 - \frac{8^{2}}{4 \cdot 1}$

Simplify the right side.

Simplify each term.

Raise $8$ to the power of $2$ .

$e = 0 - \frac{64}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 0 - \frac{64}{4}$

Divide $64$ by $4$ .

$e = 0 - 1 \cdot 16$

Multiply $- 1$ by $16$ .

$e = 0 - 16$

Subtract $16$ from $0$ .

$e = - 16$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form ${(x + 4)}^{2} - 16$ .

${(x + 4)}^{2} - 16 = y - 15$

Step 4

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

Add $16$ to both sides of the equation.

${(x + 4)}^{2} = y - 15 + 16$

Add $- 15$ and $16$ .

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

Find the Standard Form of the Parabola y=x^2+8x+15

Related Questions

Support LCMGCF.com by disabling your adblocker.