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 (0,11). (type an ordered pair.)
the axis of symmetry is \square. (simplify your answer. type an equation.)

Explanation:

Step1: Recall the formula for axis of symmetry

For a quadratic function in the form \( f(x) = ax^2 + bx + c \), the axis of symmetry is given by the equation \( x = -\frac{b}{2a} \).

Step2: Identify a and b from the function

In the function \( f(x) = x^2 - 6x + 11 \), we have \( a = 1 \) and \( b = -6 \).

Step3: Substitute a and b into the formula

Substitute \( a = 1 \) and \( b = -6 \) into \( x = -\frac{b}{2a} \):
\[
x = -\frac{-6}{2\times1} = \frac{6}{2} = 3
\]
So the axis of symmetry is the vertical line \( x = 3 \).

Answer:

\( x = 3 \)