Question

use the graph of the quadratic equation for questions 7-10.

1. describe where the parabola is increasing.
2. describe where the parabola is decreasing.
3. draw the axis of symmetry for the parabola on the graph.
4. circle the vertex, $x$-intercepts, and $y$-intercepts of the parabola. label each point as vertex, $x$-intercepts, and $y-$ intercepts.

Explanation:

Step1: Identify vertex x-coordinate

The vertex is at $x=-5$ (lowest point of parabola).

Step2: Define increasing interval

For $x > -5$, the parabola rises.

Step3: Define decreasing interval

For $x < -5$, the parabola falls.

Step4: Draw axis of symmetry

Axis of symmetry: $x=-5$ (vertical line through vertex).

Step5: Locate key points

Vertex: $(-5, -10)$
x-intercepts: $(-10, 0)$ and $(0, 0)$
y-intercept: $(0, 0)$

Answer:

1. The parabola is increasing for $x > -5$ (all real numbers greater than -5).
2. The parabola is decreasing for $x < -5$ (all real numbers less than -5).
3. A vertical line $x=-5$ (drawn through the vertex of the parabola) is the axis of symmetry.

10.

• Vertex: $(-5, -10)$ (circled)
• x-intercepts: $(-10, 0)$ and $(0, 0)$ (circled)
• y-intercept: $(0, 0)$ (circled, same as one x-intercept)