Question

find the y-coordinate of the y-intercept of the polynomial function defined below.\\( f(x) = -2(x^2 - 2) \\)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) occurs where \(x = 0\). So we need to find \(f(0)\) for the function \(f(x)=- 2(x^{2}-2)\).

Step2: Substitute \(x = 0\) into the function

Substitute \(x = 0\) into \(f(x)\):
\(f(0)=-2((0)^{2}-2)\)
First, calculate the expression inside the parentheses: \((0)^{2}-2=0 - 2=-2\)
Then, multiply by - 2: \(f(0)=-2\times(-2)\)
\(f(0) = 4\)

Answer:

4