Question

find the y-coordinate of the y-intercept of the polynomial function defined below. f(x) = 2x(x + 1)(2x + 6)(4x² - 1)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) occurs where \(x = 0\). So we need to substitute \(x = 0\) into the function \(f(x)\) and evaluate it.

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

Given \(f(x)=2x(x + 1)(2x + 6)(4x^{2}-1)\), when \(x = 0\), we have:
\(f(0)=2\times0\times(0 + 1)\times(2\times0+ 6)\times(4\times0^{2}-1)\)

Step3: Simplify the expression

First, \(2\times0 = 0\). Then, any product with a factor of 0 is 0. So \(f(0)=0\times(1)\times(6)\times(- 1)=0\).

Answer:

The \(y\) - coordinate of the \(y\) - intercept is \(0\).