Question

The graph of which function will have a maximum and a y-intercept of 4? f(x) = 4x2 + 6x – 1 f(x) = –4x2 + 8x + 5 f(x) = –x2 + 2x + 4 f(x) = x2 + 4x – 4

Answer 1

It is f(x) = -x^2 + 2x + 4.

Explanation:

As it has a maximum the coefficents of x^2 will be negative.

f(x) = -x^2 + 2x + 4

The y-intercept occurs when x = 0 so

y-intercept = 0 + 0 + 4 = 4.

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Answer 2

`f(x) = - {x}^(2) + 2x + 4`

EXPLANATION

The graph of the function that will have a maximum and a y-intercept of 4 is

`f(x) = - {x}^(2) + 2x + 4`

To check for the y-intercept, we put x=0 into the function.

`f(0) = - {0}^(2) + 2(0)+ 4`

This implies that,

`f(0) = 4`

We can see that the coefficient of the quadratic term is -1.

Since the coefficient of the quadratic term is less than zero, the graph will have a maximum point.