Find the Vertex Form 2x^2+28x-5

$2 x^{2} + 28 x - 5$

Write $2 x^{2} + 28 x - 5$ as an equation.

$y = 2 x^{2} + 28 x - 5$

Complete the square for $2 x^{2} + 28 x - 5$ .

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

$a = 2$

$b = 28$

$c = - 5$

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 $d = \frac{b}{2 a}$ .

$d = \frac{28}{2 \cdot 2}$

Simplify the right side.

Cancel the common factor of $28$ and $2$ .

Factor $2$ out of $28$ .

$d = \frac{2 \cdot 14}{2 \cdot 2}$

Cancel the common factors.

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

$d = \frac{2 \cdot 14}{2 (2)}$

Cancel the common factor.

$d = \frac{2 \cdot 14}{2 \cdot 2}$

Rewrite the expression.

$d = \frac{14}{2}$

Cancel the common factor of $14$ and $2$ .

Factor $2$ out of $14$ .

$d = \frac{2 \cdot 7}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$d = \frac{2 \cdot 7}{2 (1)}$

Cancel the common factor.

$d = \frac{2 \cdot 7}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{7}{1}$

Divide $7$ by $1$ .

$d = 7$

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

$e = - 5 - \frac{28^{2}}{4 \cdot 2}$

Simplify the right side.

Simplify each term.

Raise $28$ to the power of $2$ .

$e = - 5 - \frac{784}{4 \cdot 2}$

Multiply $4$ by $2$ .

$e = - 5 - \frac{784}{8}$

Divide $784$ by $8$ .

$e = - 5 - 1 \cdot 98$

Multiply $- 1$ by $98$ .

$e = - 5 - 98$

Subtract $98$ from $- 5$ .

$e = - 103$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $2 {(x + 7)}^{2} - 103$ .

$2 {(x + 7)}^{2} - 103$

Set $y$ equal to the new right side.

$y = 2 {(x + 7)}^{2} - 103$

Find the Vertex Form 2x^2+28x-5

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