This graph represents a parabola that opens upwards. I can help you analyze it and identify the required terms (likely items like vertex, axis of symmetry, x-intercepts, y-intercept, domain, and range). Here's the breakdown:

1. Vertex

The vertex is the lowest point of the parabola because it opens upward. From the graph:

• Vertex: $(-5, -9)$

2. Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two symmetric halves.

• Axis of Symmetry: $x = -5$

3. X-Intercepts

The x-intercepts are where the parabola crosses the x-axis (i.e., $y = 0$). From the graph:

• X-Intercepts: $(-10, 0)$ and $(0, 0)$

4. Y-Intercept

The y-intercept is where the parabola crosses the y-axis (i.e., $x = 0$). From the graph:

• Y-Intercept: $(0, 0)$

5. Domain and Range

• Domain: Since the parabola extends infinitely left and right, the domain is $(-\infty, \infty)$.
• Range: Since the vertex is at $y = -9$ and the parabola opens upward, the range is $[-9, \infty)$.

Would you like more details or help solving further related questions?

Here are 5 related questions you might explore:

1. What is the standard form of the quadratic equation for this parabola?
2. How do you determine the vertex algebraically?
3. What transformations could result in this parabola?
4. How do you find the x-intercepts using factoring?
5. How does the range of this parabola change if it opens downward?

Tip: The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.