# Question #5f4a4

Oct 4, 2017

The vertex form is $y = 4 {\left(x + 3\right)}^{2} - 36$, with vertex at $\left(- 3 , - 36\right)$.

#### Explanation:

You should start by completing the square.

$y = 4 \left({x}^{2} + 6 x + n - n\right)$

The value of $n$ will be given by $n = {\left(\frac{b}{2}\right)}^{2}$, where $b$ is the middle term in the parentheses, the $6$ in this case.

$n = {\left(\frac{6}{2}\right)}^{2} = 9$

Therefore:

$y = 4 \left({x}^{2} + 6 x + 9 - 9\right)$

$y = 4 \left({x}^{2} + 6 x + 9\right) - 9 \left(4\right)$

$y = 4 {\left(x + 3\right)}^{2} - 36$

The vertex of a quadratic of the form $y = a {\left(x - p\right)}^{2} + q$ is given by $\left(p , q\right)$. Therefore, the vertex is $\left(- 3 , - 36\right)$.

The graph of the parabola confirms.
graph{4x^2 + 24x [-103.2, 103.2, -51.6, 51.6]}

Hopefully this helps!