Find the Vertex Form y=-6x^2-24x-25

$y = - 6 x^{2} - 24 x - 25$

Step 1

Complete the square for $- 6 x^{2} - 24 x - 25$ .

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

$a = - 6$

$b = - 24$

$c = - 25$

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

$d = \frac{- 24}{2 \cdot - 6}$

Simplify the right side.

Cancel the common factor of $- 24$ and $2$ .

Factor $2$ out of $- 24$ .

$d = \frac{2 \cdot - 12}{2 \cdot - 6}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 6$ .

$d = \frac{2 \cdot - 12}{2 (- 6)}$

Cancel the common factor.

$d = \frac{2 \cdot - 12}{2 \cdot - 6}$

Rewrite the expression.

$d = \frac{- 12}{- 6}$

Cancel the common factor of $- 12$ and $- 6$ .

Factor $- 6$ out of $- 12$ .

$d = \frac{- 6 (2)}{- 6}$

Cancel the common factors.

Factor $- 6$ out of $- 6$ .

$d = \frac{- 6 \cdot 2}{- 6 \cdot 1}$

Cancel the common factor.

$d = \frac{- 6 \cdot 2}{- 6 \cdot 1}$

Rewrite the expression.

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

Divide $2$ by $1$ .

$d = 2$

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

$e = - 25 - \frac{{(- 24)}^{2}}{4 \cdot - 6}$

Simplify the right side.

Simplify each term.

Raise $- 24$ to the power of $2$ .

$e = - 25 - \frac{576}{4 \cdot - 6}$

Multiply $4$ by $- 6$ .

$e = - 25 - \frac{576}{- 24}$

Divide $576$ by $- 24$ .

$e = - 25 - - 24$

Multiply $- 1$ by $- 24$ .

$e = - 25 + 24$

Add $- 25$ and $24$ .

$e = - 1$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- 6 {(x + 2)}^{2} - 1$ .

$- 6 {(x + 2)}^{2} - 1$

Step 2

Set $y$ equal to the new right side.

$y = - 6 {(x + 2)}^{2} - 1$

Find the Vertex Form y=-6x^2-24x-25

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