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

Option C (f(x) =
`-x^2 + 2x + 4`)

Explanation:

In this question, the first step is to write the general form of the quadratic equation, which is f(x) =
`ax^2 + bx + c`, where a, b, and c are the arbitrary constants. There are certain characteristics of the values of a, b, and c which determine the nature of the function. If a is a positive coefficient (i.e. if a>0), then the quadratic function is a minimizing function. On the other hand, a is negative (i.e. if a<0), then the quadratic function is a maximizing function. Since the latter condition is required, therefore, the first option and the last option are incorrect. The features of the values of b are irrelevant in this question, so that will not be discussed here. The value of c is actually the y-intercept of the quadratic equation. Since the y-intercept is 4, the correct choice for this question will be Option C. In short, Option C fulfills both the criteria of the function which has a maximum and a y-intercept of 4!!!