Determine whether the following quadratic function has a max

Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occurs. H(x) = -5x^2 + 12x + 1 Select the correct choice below and fill in the answer boxes to complete your choice. (Simplify your answers) The function has a maximum value of at x= The function has a minimum value of at x=

Solution

f(x) = -5x^2 +12x +1

parabola is upward facing as a <0 ; a = -5

So, f(x) would have a maxima:

Maxima would occur at vertex: (h, k)

h = -b/2a = -(12/-10) = 1.2

k =-5(1.2)^2 +12(1.2) +1 = 8.2

Vertex ( 1.2 , 8.2)

Maximum value of 8.2 occurs at x = 1.2