The standard form of the equation of a parabola is #y=2x^2+16x+17#. What is the vertex form of the equation?

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Answer 1 · 2017-03-23T19:41:47

The general vertex form is #y = a(x-h)^2+k#. Please see the explanation for the specific vertex form.

The "a" in the general form is the coefficient of the square term in the standard form:

#a = 2#

The x coordinate in of the vertex, h, is found using the formula:

#h = -b/(2a)#

#h = -16/(2(2)#

#h = -4#

The y coordinate of the vertex, k, is found by evaluating the given function at #x = h#:

#k = 2(-4)^2+16(-4)+17#

#k = -15#

Substituting the values into the general form:

#y = 2(x--4)^2-15 larr# the specific vertex form