SOLUTION: f(x)=-2x^2+8x-12 does the function have a minimum or maximum value? where does the minimum or maximum value occur? what is the functions minum or maximum value?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: f(x)=-2x^2+8x-12 does the function have a minimum or maximum value? where does the minimum or maximum value occur? what is the functions minum or maximum value?      Log On


   

Question 933677: f(x)=-2x^2+8x-12 does the function have a minimum or maximum value? where does the minimum or maximum value occur? what is the functions minum or maximum value?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-2x%5E2%2B8x-12 does the function have a minimum or maximum value?
There is an negative coefficient -2 (means a%3C0 ) in front of x%5E2 term, so this is a parabola that opens downwards and has a maximum.
a maximum is the vertex and the vertex form of equation is:
y+=+a%28x-h%29%5E2%2Bk, where (h,k) is the vertex

Put f%28x%29=-2x%5E2%2B8x-12 into vertex form.
f%28x%29=-2x%5E2%2B8x-12
f%28x%29=-2%28x%5E2-4x%29-12...complete the square
f%28x%29=-2%28x%5E2-4x%2B___%29-%28-2%29___-12
f%28x%29=-2%28x%5E2-4x%2B2%5E2%29-%28-2%292%5E2-12
f%28x%29=-2%28x-2%29%5E2%2B8-12
f%28x%29=-2%28x-2%29%5E2-4
vertex (h,k) = (2,-4)