Question

what is the y-intercept of the function?
$f(x)=3x^{2}+4x + 5$
the y-intercept is \square. (type an ordered pair, using integers or decimals.)

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is the point where the graph of the function intersects the y - axis. On the y - axis, the \(x\) - coordinate is \(0\). So, to find the y - intercept, we substitute \(x = 0\) into the function \(f(x)\).

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

Given the function \(f(x)=3x^{2}+4x + 5\), when \(x = 0\), we have:
\(f(0)=3(0)^{2}+4(0)+5\)
First, calculate \(3(0)^{2}=0\) and \(4(0) = 0\). Then, \(f(0)=0 + 0+5=5\).

The ordered pair for the y - intercept is \((0,f(0))=(0,5)\).

Answer:

\((0, 5)\)