Question

Given a function with a y-intercept of (0, -2) and a vertex of (-4, 1), determine the function.

a) f(x)=−(x+4)² +1
b) f(x)=−(x-4)² +1
c) f(x)=−(x+4)² -1
d) f(x)=−(x-4)²-1

Answer 1

The function is f(x) = - (x + 4)^2 + 1.

Step-by-step explanation:

In order to determine the function with a y-intercept of (0, -2) and a vertex of (-4, 1), we can use the standard form of a quadratic function, f(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Plugging in the given values, we have f(x) = a(x + 4)^2 + 1. Comparing this with the options provided, the correct answer is f(x) = - (x + 4)^2 + 1 (option a).