Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function.
$f(x)=x^{2}-4x + 19$
the y - intercept is (0, 19). (type an ordered pair.)
the axis of symmetry is
(simplify your answer. type an equation.)

Explanation:

Step1: Recall the formula for the axis of symmetry of a quadratic function

For a quadratic function in the form \( f(x) = ax^2 + bx + c \), the equation of the axis of symmetry is given by \( x = -\frac{b}{2a} \).
In the function \( f(x) = x^2 - 4x + 19 \), we have \( a = 1 \) and \( b = -4 \).

Step2: Substitute the values of \( a \) and \( b \) into the formula

Substitute \( a = 1 \) and \( b = -4 \) into \( x = -\frac{b}{2a} \):
\( x = -\frac{-4}{2\times1} \)
Simplify the numerator and the denominator:
\( x = \frac{4}{2} \)
\( x = 2 \)

Answer:

The axis of symmetry is the line \( x = 2 \)