Adding Quadratic Functions

Question

Suppose f(x) is a quadratic function with an absolute minimum and g(x) is a quadratic function with an absolute maximum.

We then have a third quadratic function (g+f)(x)

Explain how you would go about determining whether this new function has an absolute minimum or absolute maximum.

Answer 1

f(x)=x^2, g(x)=-x^2

f+g = 0, which is bot an absolute max and min

f(x)=2x^2, g(x)=-x^2

f+g=x^2 has an absolute minimum

f(x)=x^2, g(x)=-2x^2

f+g=-x^2 has an absolute maximum

look at the coefficient of the x^2 term of f+g.

if >0 then abs min.

if <0 abs max,

if 0 both,if a flat line

or neither if a sloped line or vertical