SOLUTION: Find the minimum value of the quadratic y = 2x^2 - 8x + 8. At what x-value does the minimum occur? State the domain and range of this function. Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the minimum value of the quadratic y = 2x^2 - 8x + 8. At what x-value does the minimum occur? State the domain and range of this function. Thank you.       Log On


   

Question 1188441: Find the minimum value of the quadratic y = 2x^2 - 8x + 8. At what x-value does the minimum occur? State the domain and range of this function. Thank you.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+2x%5E2+-+8x+%2B+8
At what x-value does the minimum occur?
since you have a parabola that opens up, minimum is at vertex; so, complete square and write equation in vertex form
y+=+%282x%5E2+-+8x+%29%2B+8
y+=+2%28x%5E2+-+4x+%29%2B+8
y+=+2%28x%5E2+-+4x+%2Bb%5E2%29-2b%5E2%2B+8........b=4%2F2=2
y+=+2%28x%5E2+-+4x+%2B2%5E2%29-2%2A2%5E2%2B+8
y+=+2%28x-+2%29%5E2-2%2A4%2B+8
y+=+2%28x-+2%29%5E2-8%2B+8
y+=+2%28x-+2%29%5E2+=> vertex is at (2,0)
so, minimum is 0 at x=2

domain: R (all real numbers)
range:{ y element R : y%3E=0 } (all non-negative real numbers)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2+-+8x+%2B+8%29+