Question

Question #5f4a4

Answer 1

The vertex form is `y = 4(x + 3)^2 - 36`, with vertex at `(-3, -36)`.

Explanation:

You should start by completing the square.

`y = 4(x^2 + 6x + n - n)`

The value of `n` will be given by `n = (b/2)^2`, where `b` is the middle term in the parentheses, the `6` in this case.

`n = (6/2)^2 = 9`

Therefore:

`y = 4(x^2 + 6x + 9 - 9)`

`y = 4(x^2 + 6x + 9) - 9(4)`

`y = 4(x + 3)^2 - 36`

The vertex of a quadratic of the form `y = a(x - p)^2 + q` is given by `(p, q)`. Therefore, the vertex is `(-3, -36)`.

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

Hopefully this helps!