Question

Determine whether F(x)=4x^2-16x+6 has a maximum or a minimum value and find that value

Answer 1

f(x) has a minimum value of -10.

Explanation:

It will have a minimum value because the coefficient of x^2 is positive.

To find its value we convert to vertex form:

f(x) = 4x^2 - 16x + 6

= 4(x^2 - 4x) + 6

= 4[(x - 2)^2 - 4] + 6

= 4(x - 2)^2 - 16 + 6

= 4(x - 2)^2 - 10.

So the minimum value is -10.