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

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

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

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

Answer 1

Answer:

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

Explanation:

After observation, graph of function 1 has vertex at Maximum (4, 1)

In order to find vertex of function 2, complete square the equation.

f(x) = -x² + 2x - 3

f(x) = -(x² - 2x) - 3

f(x) = -(x - 1)² - 3 + (-1)²

f(x) = -(x - 1)² - 2

Vertex form: y = a(x - h)² + k where (h, k) is the vertex

So, here for function 2 vertex: Maximum (1, -2)

Conclusion:

Function 1 = Maximum (4, 1), Function 2 = Maximum (1, -2)

Function 1 has greater maximum value of (4, 1) as "1 is greater than -2"