Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function f(x) = x² - 4x + 19. the y - intercept is (0, 19). (type an ordered pair.) the axis of symmetry is x = 2. (simplify your answer. type an equation.) the vertex is \square. (type an ordered pair)

Explanation:

Step1: Recall the vertex formula for a quadratic function

For a quadratic function \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex is given by \( x = -\frac{b}{2a} \). Here, \( a = 1 \), \( b = -4 \), so \( x = -\frac{-4}{2\times1} = 2 \).

Step2: Find the y-coordinate of the vertex

Substitute \( x = 2 \) into the function \( f(x) = x^2 - 4x + 19 \). So \( f(2) = 2^2 - 4\times2 + 19 = 4 - 8 + 19 = 15 \).

Answer:

\((2, 15)\)