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) = −x2 + 2x − 3

Function has the larger maximum.

(Put 1 or 2 in the blank space)

Function 1 written in vertex form is f(x) = -x^2 + 8x - 15 = -(x^2 - 8x + 15) = -(x^2 - 8x + 16 + 15 - 16) = -(x - 4)^2 - (-1) = -(x - 4)^2 + 1

Therefore, vertex = (4, 1)

Function 2 written in vertex form is f(x) = -x^2 + 4x + 1 = -(x^2 - 4x - 1) = -(x^2 - 4x + 4 - 1 - 4) = -(x - 2)^2 - (-5) = -(x - 2)^2 + 5

Therefore vertex = (2, 5)

Function 1 has a maximum at y = 1 and function 2 has a maximum at y = 5. Therefore, function 2 has a larger maximum.

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