Question

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

Function 1

graph of function f of x equals negative x squared plus 8 multiplied by x minus 15

Function 2

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

Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)

Answer 1

I can confirm that the answer above is correct because I took the test and got it right.

Explanation:

The answer is:

Function 2 has the larger maximum.

Answer 2

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.