What is the vertex form of # f(x) = -2x^2+7x-12 #?

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Answer 1 · 2017-03-25T16:43:27

Given the standard form of a parabola:

#f(x)=ax^2+bx+c#

The vertex form is:

#f(x)=a(x-h)^2+k#

Please see the explanation for the conversion process.

Given the specific equation in standard form:

#f(x) = -2x^2+7x-12#

Here is the graph:

graph{-2x^2+7x-12 [-26.5, 38.46, -33.24, 0.58]}

Comparing with the standard form:

#a = -2, b = 7, and c = -12#

You obtain the value of "a" by observation:

#a = -2#

To obtain the value of h, use the equation:

#h = -b/(2a)#

#h = -7/(2(-2)#

#h = 7/4#

To obtain the value of k, evaluate the function at #x = h#:

#k = -2(7/4)^2+7(7/4)-12#

#k = -94/16#

Substituting these values into the vertex form:

#f(x) = -2(x-7/4)^2-94/16#