Question

find the y-intercept, the axis of symmetry, and the vertex of the graph of the function.
$f(x)=x^{2}-6x + 11$
the y-intercept is \square. (type an ordered pair.)

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the point where \( x = 0 \). So we substitute \( x = 0 \) into the function \( f(x)=x^{2}-6x + 11 \).

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

When \( x = 0 \), we have \( f(0)=0^{2}-6\times0 + 11 \).
Simplify the expression: \( f(0)=0 - 0+11=11 \).
So the y - intercept is the ordered pair \( (0,11) \) since \( x = 0 \) and \( y=f(0) = 11 \).

Answer:

\((0, 11)\)