The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair.

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 - 15

Function 1 has the larger maximum at (4, 1).

Function 1 has the larger maximum at (1, 4).

Function 2 has the larger maximum at (-14, 1).

Function 2 has the larger maximum at (1, - 14).

Correct option: First one - > Function 1 has the larger maximum at (4, 1).

Step-by-step explanation:

Function 1:

f (x) = - x2 + 8x - 15

To find the x-coordinate of the vertix, we can use the formula:

x_v = - b/2a

x_v = - 8 / (-2) = 4

Then, to find the maximum value of f (x), we use the value of x = x_v:

f (x_v) = - 4^2 + 8*4 - 15 = 1

Maximum of f (x) : (4,1)

Function 2:

f (x) = - x2 + 2x - 15

To find the x-coordinate of the vertix, we can use the formula:

x_v = - b/2a

x_v = - 2 / (-2) = 1

Then, to find the maximum value of f (x), we use the value of x = x_v:

f (x_v) = - 1^2 + 2*1 - 15 = - 14

Maximum of f (x) : (1,-14)

The maximum value of function 1 is greater than the maximum of function 2 (1 is greater than - 14).

Correct option: First one