Let's go through the problem in your image step by step.

(a) Does the parabola open upward or downward?

• Since the parabola's vertex is at the top and the arms extend downward, it opens downward.

(b) Find the equation of the axis of symmetry

• The axis of symmetry is the vertical line that passes through the vertex. This line's equation is of the form $x = h$, where $h$ is the x-coordinate of the vertex.
• From the graph, the x-coordinate of the vertex seems to be around $x = 2$, so the axis of symmetry is: $\text{Axis of symmetry: } x = 2$

(c) Find the coordinates of the vertex

• The vertex is the highest point of the parabola. From the graph, it looks like the vertex is at the point $(2, 4)$. $\text{Vertex: } (2, 4)$

(d) Find the intercept(s)

1. x-intercepts: These are the points where the parabola crosses the x-axis. It seems the parabola crosses the x-axis at $x = 0$ and $x = 4$. $\text{x-intercepts: } 0, 4$
2. y-intercept: The parabola crosses the y-axis at $y = 0$, so: $\text{y-intercept: } (0, 0)$

Would you like more details or clarification on any part of this solution?

Additional Questions:

1. How do you determine whether a parabola opens upward or downward based on its graph?
2. What is the significance of the axis of symmetry for a parabola?
3. How can you find the vertex of a parabola using its equation in standard form?
4. How would you calculate x-intercepts algebraically if the equation of the parabola is given?
5. How is the vertex related to the maximum or minimum value of a quadratic function?

Tip:

When finding the axis of symmetry, it always corresponds to the x-value of the vertex of the parabola, regardless of whether it opens upward or downward.