Question

find the y-intercept, the axis of symmetry, and the vertex of the graph of the function. f(x) = -3x² + 6x - 2 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 value of \(x=0\). So we substitute \(x = 0\) into the function \(f(x)=-3x^{2}+6x - 2\).

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

When \(x = 0\), we have \(f(0)=-3(0)^{2}+6(0)-2\).
First, calculate each term: \(-3(0)^{2}=0\), \(6(0) = 0\). Then \(f(0)=0 + 0-2=-2\).

So the y - intercept is the ordered pair \((0,-2)\) because when \(x = 0\), \(y=-2\).

Answer:

\((0, - 2)\)