Let's analyze the given graph and answer each part of the question:

(a) Does the parabola open upward or downward?

From the graph, the parabola opens upward.

(b) Find the intercept(s).

• x-intercept(s): The parabola crosses the x-axis at two points, approximately around $(-8, 0)$ and $(0, 0)$.

  Therefore, the x-intercepts are: -8, 0

• y-intercept(s): The parabola crosses the y-axis at $(0, 0)$.

  Therefore, the y-intercept is: 0

(c) Find the coordinates of the vertex.

The vertex, which is the lowest point on the parabola since it opens upward, appears to be at approximately $(-4, -10)$.

So, the vertex is: (-4, -10)

(d) Find the equation of the axis of symmetry.

The axis of symmetry of a parabola passes through its vertex and is vertical. Given the vertex at $(-4, -10)$, the axis of symmetry is the vertical line:

x = -4

Let me know if you would like more details or have any questions!

Related Questions

1. What is the general form of a quadratic equation that represents a parabola?
2. How do we determine whether a parabola opens upwards or downwards from its equation?
3. How do the x-intercepts relate to the factors of the quadratic equation of the parabola?
4. What is the vertex form of a parabola, and how does it help in identifying the vertex?
5. How can we calculate the axis of symmetry from a given quadratic function?

Tip

To quickly find the axis of symmetry of a parabola given by $y = ax^2 + bx + c$, use the formula $x = -\frac{b}{2a}$.