SOLUTION: Find the maximum or minimum of the function f(x)=8x^2-4x+50.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the maximum or minimum of the function f(x)=8x^2-4x+50.       Log On


   

Question 368460: Find the maximum or minimum of the function f(x)=8x^2-4x+50.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Convert to vertex form, y=a%28x-h%29%5E2%2Bk, by completing the square.
f%28x%29=8x%5E2-4x%2B50
f%28x%29=8%28x%5E2-%281%2F2%29x%29%2B50
f%28x%29=8%28x%5E2-%281%2F2%29x%2B1%2F16%29%2B50-8%2F16
f%28x%29=8%28x-1%2F4%29%5E2%2B100%2F2-1%2F2
f%28x%29=8%28x-1%2F4%29%5E2%2B99%2F2
The maximum/minimum occurs at the vertex.
Since a=8%3E0, the parabola opens upwards and the vertex value is a minimum.
y%5Bmin%5D=99%2F2