Question

Consider the quadratic function f(x)=1/2x^2+2x-6. express f in vertex form find the extreme value and classify it as a local maximum or local minimum. Consider the quadratic function f(x)=1/2x^2+2x-6. express f in vertex form find the extreme value and classify it as a local maximum or local minimum. @Mathematics

Answer 1

to express it in vertex form you need to make it look like this:

f(x) = A*(x-h)^2+k

so first factor out a 1/2...

f(x) = 1/2(x^2+4x-12)

now factor the parenthesis by completing the square.

f(x) = 1/2*(x^2 + 4x - 12 +4 -4)

f(x) = 1/2*(x+2)^2-8

This is vertex form.. where the vertex is (-2,-8)

This is a local minimum because the graph opens up.