Question

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).

Answer 1

a

Explanation:

Answer 2

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

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