Let's analyze the provided graph of the parabola and answer each part step by step:

(a) Does the parabola open upward or downward?

• The parabola opens upward because its arms are facing upwards.

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

• The axis of symmetry is a vertical line that passes through the vertex of the parabola.
• From the graph, the vertex appears to be located at $x = -2$.
• Thus, the equation of the axis of symmetry is:
  $x = -2$

(c) Find the intercept(s).

1. X-intercept(s):

   • The parabola crosses the x-axis at two points. By checking the graph, the x-intercepts are at $x = -4$ and $x = 0$.
   • So, the x-intercepts are:
     $-4, 0$

2. Y-intercept(s):

   • The y-intercept is the point where the parabola crosses the y-axis.
   • From the graph, the parabola crosses the y-axis at $y = 4$.
   • So, the y-intercept is:
     $4$

(d) Find the coordinates of the vertex.

• From the graph, the vertex is the minimum point of the parabola. It is located at:
  $(-2, 4)$

Final Answers:

• (a) Upward
• (b) Equation of axis of symmetry: $x = -2$
• (c) X-intercepts: -4, 0
  Y-intercept: 4
• (d) Vertex: $(-2, 4)$

Let me know if you would like a detailed explanation for any part!

Related Questions:

1. How do you determine the axis of symmetry from a quadratic equation?
2. What is the general formula for finding the vertex of a parabola?
3. Can a parabola have no x-intercepts? Explain why.
4. What does the y-coordinate of the vertex represent in a parabola?
5. How do you determine if a parabola opens upward or downward from its equation?

Tip:

The vertex form of a quadratic equation, $y = a(x - h)^2 + k$, makes it easy to identify the vertex $(h, k)$.