Question #ea797

1 Answer
Douglas K.
Jan 27, 2017

The vertex form of the equation of a vertically oriented parabola is:
#y = a(x - h)^2 + k# where a is the coefficient of the #x^2# term and #(h,k)# is the vertex

Explanation:

Given: #y = -2x^2 - 16x -32#

Please observe that #a = -2#

Add zero to the right side of the equation in form of #ah^2 - ah^2#:

#y = -2x^2 - 16x + -2h^2 - -2h^2 -32#

Factor -2 out of the first three terms on the right:

#y = -2(x^2 + 8x + h^2) + 2h^2 -32#

Using the pattern #(x - h)^2 = x^2 - 2hx + h^2#, we set the middle term in the right side of the pattern equal to middle term in the equation:

#-2hx = 8x#

#h = -4#

Substitute the left side of the pattern into the equation:

#y = -2(x - h)^2 + 2h^2 -32#

Substitute - 4 for h:

#y = -2(x - -4)^2 + 2(-4)^2 -32#

Combine the constant terms:

#y = -2(x - -4)^2#

This is the vertex form.

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