Question

The following graph describes function 1 and the equation below it describes function 2:

Answer 1

Function 1: 
f(x) = -x² + 8(x-15)f(x) = -x² + 8x - 120
Function 2:
f(x) = -x² + 4x+1
Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.
Function 1 derivative: -2x + 8 ⇒ -2x + 8 = 0 ⇒ - 2x = -8 ⇒ x = -8/-2 = 4

Function 2 derivative:  -2x+4 ⇒ -2x + 4 = 0 ⇒ -2x = -4 ⇒ x = -4/-2 ⇒  x= 2
Function 1: f(x) = -x² + 8x - 120 ; x = 4
f(4) = -4² + 8(4) - 120 = 16 + 32 - 120 = -72

Function 2: f(x) = -x² + 4x+1 ; x = 2
f(2) = -2² + 4(2) + 1 = 4 + 8 + 1 = 13

Function 2 has the larger maximum.