Question #5f4a4

Question

1824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-04T17:18:41

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

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

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!