Question

sketch the graph of the quadratic function and the axis of symmetry. state the vertex, and give the equation for the axis of symmetry
f(x) = -(x - 3)²

use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
graph with click to enlarge graph text

what is the vertex of the graph?
the vertex is
(type an ordered pair)

what is the equation of the axis of symmetry?

(type an equation)

Explanation:

Step1: Recall vertex form of quadratic

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
For \( f(x) = -(x - 3)^2 \), we can rewrite it as \( f(x) = -1(x - 3)^2 + 0 \).

Step2: Identify vertex

From the vertex form, \( h = 3 \) and \( k = 0 \), so the vertex is \((3, 0)\).

Step3: Determine axis of symmetry

The axis of symmetry for a quadratic in vertex form \( f(x) = a(x - h)^2 + k \) is the vertical line \( x = h \).
Since \( h = 3 \), the axis of symmetry is \( x = 3 \).

Answer:

The vertex is \((3, 0)\).
The equation of the axis of symmetry is \( x = 3 \).