Let me analyze the graph from your uploaded image and solve the problems step by step.

(a) Does the parabola open upward or downward?

From the graph, the parabola opens upward, as the curve has a U-shape with the arms extending upwards.

(b) Find the intercept(s):

1. X-intercept(s):

   • The x-intercepts are the points where the parabola crosses the x-axis.
   • From the graph, these points appear to be approximately (-2, 0) and (2, 0).

   So, the x-intercepts are: -2, 2.

2. Y-intercept(s):

   • The y-intercept is the point where the parabola crosses the y-axis.
   • From the graph, this point is at (0, -4).

   So, the y-intercept is: -4.

(c) Find the coordinates of the vertex:

The vertex is the lowest point on the graph, as the parabola opens upwards. From the graph, the vertex is located at (0, -4).

So, the vertex is: (0, -4).

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

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (0, -4), the equation of the axis of symmetry is:

x = 0.

Final Answers:

• (a) Parabola opens upward.
• (b) Intercepts:
  • X-intercepts: -2, 2
  • Y-intercept: -4
• (c) Vertex: (0, -4)
• (d) Axis of symmetry: x = 0

Would you like me to explain any step in greater detail?

Related Questions:

1. How do you find the vertex algebraically from a quadratic equation?
2. What is the significance of the axis of symmetry in a parabola?
3. How can we calculate intercepts without a graph?
4. What is the relationship between the vertex and the direction a parabola opens?
5. Can a parabola have more than two x-intercepts?

Tip:

To confirm your vertex and axis of symmetry, always check if the parabola is symmetrical about the line $x = h$, where $h$ is the x-coordinate of the vertex.