Find the Vertex y=-6x^2-12x-1

$y = - 6 x^{2} - 12 x - 1$

Rewrite the equation in vertex form.

Complete the square for $- 6 x^{2} - 12 x - 1$ .

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

$a = - 6$

$b = - 12$

$c = - 1$

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

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

Simplify the right side.

Cancel the common factor of $- 12$ and $2$ .

Factor $2$ out of $- 12$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

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

$e = - 1 - \frac{{(- 12)}^{2}}{4 \cdot - 6}$

Simplify the right side.

Simplify each term.

Raise $- 12$ to the power of $2$ .

$e = - 1 - \frac{144}{4 \cdot - 6}$

Multiply $4$ by $- 6$ .

$e = - 1 - \frac{144}{- 24}$

Divide $144$ by $- 24$ .

$e = - 1 - - 6$

Multiply $- 1$ by $- 6$ .

$e = - 1 + 6$

Add $- 1$ and $6$ .

$e = 5$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- 6 {(x + 1)}^{2} + 5$ .

$- 6 {(x + 1)}^{2} + 5$

Set $y$ equal to the new right side.

$y = - 6 {(x + 1)}^{2} + 5$

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = - 6$

$h = - 1$

$k = 5$

Find the vertex $(h, k)$ .

$(- 1, 5)$

Find the Vertex y=-6x^2-12x-1

Related Questions

Support LCMGCF.com by disabling your adblocker.