Question

question
find the y - coordinate of the y - intercept of the polynomial function defined below.
$f(x) = 2x(x + 1)(2x + 6)(4x^2 - 1)$

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 given polynomial function.

Step2: Substitute \(x = 0\) into \(f(x)\)

Substitute \(x = 0\) into \(f(x)=2x(x + 1)(2x + 6)(4x^{2}-1)\):
\[

$$\begin{align*} f(0)&=2\times0\times(0 + 1)\times(2\times0+ 6)\times(4\times0^{2}-1)\\ &=2\times0\times1\times6\times(- 1) \end{align*}$$

\]

Step3: Simplify the expression

Any number multiplied by 0 is 0. So \(2\times0\times1\times6\times(-1)=0\).

Answer:

0