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 1graph of function f of x equals negative x squared plus 8 multiplied by x minus 15Function 2f(x) = −x2 + 2x − 15Group of answer choicesFunction 2 has the larger maximum at (−14, 1).Function 1 has the larger maximum at (1, 4).Function 2 has the larger maximum at (1, −14).Function 1 has the larger maximum at (4, 1).

Answer 1

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

Step-by-step explanation:

Function 1

The maximum is the highest point on the graph. Looking at the graph, the coordinates of the vertex are x = 4 and y = 1

The maximum value is 1

Function 2

The standard form of a quadratic equation is expressed as

y = ax^2 + bx + c

The formula for calculating the x coordinate of the vertex is expressed as

x = - b/2a

From the given function,

a = - 1

b = 2

c = - 15

Thus,

x = - 2/2 * - 1 = - 2/- 2 = 1

We would find the y intercept of the vertex by substituting x = 1 into the equation. We have

y = - (1)^2 + 2(1) - 15

y = 1 + 2 - 15

y = - 12

The maximum value is - 12

Since 1 is greater than - 12,

the graph has a greater maximum. The ordered pair is (4, 1)