Question

Write the quadratic function in the form f (x) = a (x - h) ^2 + k . Then, give the vertex of its graph. f (x) = -x ^2 + 8x -12

Writing in the form specified: f (x) = ____
Vertex: ( _ , _ )

Answer 1

complete the square

first group the x terms
f(x)=(-x²+8x)-12
facotr out quadratic coefient (number in front of the x² term is -1)
f(x)=-1(x²-8x)-12
take 1/2 of linear coefient and square it
-8/2=-4, (-4)²=16
add positive and negative inside parentahsees
f(x)=-1(x²-8x+16-16)-12
factor perfect square
f(x)=-1((x-4)²-16)-14
expand
f(x)=-1(x-4)²+16-14
f(x)=-1(x-4)²+2

vertex is (4,2)
vertex form is f(x)=-1(x-4)²+2
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