Find the Vertex Form 4x^2+88x

$4 x^{2} + 88 x$

Step 1

Write $4 x^{2} + 88 x$ as an equation.

$y = 4 x^{2} + 88 x$

Step 2

Complete the square for $4 x^{2} + 88 x$ .

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

$a = 4$

$b = 88$

$c = 0$

Consider the vertex form of a parabola.

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

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

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

$d = \frac{88}{2 \cdot 4}$

Simplify the right side.

Cancel the common factor of $88$ and $2$ .

Factor $2$ out of $88$ .

$d = \frac{2 \cdot 44}{2 \cdot 4}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 4$ .

$d = \frac{2 \cdot 44}{2 (4)}$

Cancel the common factor.

$d = \frac{2 \cdot 44}{2 \cdot 4}$

Rewrite the expression.

$d = \frac{44}{4}$

Cancel the common factor of $44$ and $4$ .

Factor $4$ out of $44$ .

$d = \frac{4 \cdot 11}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$d = \frac{4 \cdot 11}{4 (1)}$

Cancel the common factor.

$d = \frac{4 \cdot 11}{4 \cdot 1}$

Rewrite the expression.

$d = \frac{11}{1}$

Divide $11$ by $1$ .

$d = 11$

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

$e = 0 - \frac{88^{2}}{4 \cdot 4}$

Simplify the right side.

Simplify each term.

Raise $88$ to the power of $2$ .

$e = 0 - \frac{7744}{4 \cdot 4}$

Multiply $4$ by $4$ .

$e = 0 - \frac{7744}{16}$

Divide $7744$ by $16$ .

$e = 0 - 1 \cdot 484$

Multiply $- 1$ by $484$ .

$e = 0 - 484$

Subtract $484$ from $0$ .

$e = - 484$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $4 {(x + 11)}^{2} - 484$ .

$4 {(x + 11)}^{2} - 484$

Step 3

Set $y$ equal to the new right side.

$y = 4 {(x + 11)}^{2} - 484$

Find the Vertex Form 4x^2+88x

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