Question

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 4x 1 function ____ has the larger maximum. (put 1 or 2 in the blank space) numerical answers expected! answer for blank 1:

Answer 1

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.

Answer 2

The function 2 represented by the equation f(x) = -(x - 2)² + 5 has the larger maximum

How to complete the blank spaces?

The functions are given as:

Function 1

f(x) = -(x - 4)² + 1

Function 2:

f(x) = -(x - 2)² + 5

A quadratic function is represented as:

f(x) = a(x - h)² + k

When a is negative then, the vertex of the function is a maximum

In both functions, the value of a is -1

This means that both functions are at a maximum

The values of k in both functions are:

Function 1: k = 1

Function 2: k = 5

By comparison. 5 is greater than 1

Hence, function 2 has the larger maximum

Read more about quadratic functions at:

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