Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function.
$f(x) = 3x^2 + 24x + 7$
the y - intercept is \boxed{}. (type an ordered pair.)

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 \(f(x)=3x^{2}+24x + 7\), when \(x = 0\), we have:
\(f(0)=3(0)^{2}+24(0)+7\)
First, calculate \(3(0)^{2}=3\times0 = 0\), \(24(0)=0\). Then, \(f(0)=0 + 0+7=7\).

Since the x - coordinate of the y - intercept is \(0\) and the y - coordinate is \(f(0) = 7\), the y - intercept is the ordered pair \((0,7)\).

Answer:

\((0, 7)\)