Question #5f4a4

1 Answer
Oct 4, 2017

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!