Find the Vertex Form y=7x^2+14x+4

$y = 7 x^{2} + 14 x + 4$

Step 1

Complete the square for $7 x^{2} + 14 x + 4$ .

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

$a = 7$

$b = 14$

$c = 4$

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

$d = \frac{14}{2 \cdot 7}$

Simplify the right side.

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

Factor $2$ out of $14$ .

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

Cancel the common factors.

Factor $2$ out of $2 \cdot 7$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $7$ .

Cancel the common factor.

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

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

$e = 4 - \frac{14^{2}}{4 \cdot 7}$

Simplify the right side.

Simplify each term.

Raise $14$ to the power of $2$ .

$e = 4 - \frac{196}{4 \cdot 7}$

Multiply $4$ by $7$ .

$e = 4 - \frac{196}{28}$

Divide $196$ by $28$ .

$e = 4 - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$e = 4 - 7$

Subtract $7$ from $4$ .

$e = - 3$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $7 {(x + 1)}^{2} - 3$ .

$7 {(x + 1)}^{2} - 3$

Step 2

Set $y$ equal to the new right side.

$y = 7 {(x + 1)}^{2} - 3$

Find the Vertex Form y=7x^2+14x+4

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