Let's break down the questions and analyze the graph to fill in the required information.

(a) Does the parabola open upward or downward?

• Based on the shape of the graph, we can see that the parabola opens upward or downward depending on whether it is facing upwards or downwards.

(b) Find the intercept(s):

• X-intercept(s): These are the points where the graph crosses the x-axis.
• Y-intercept(s): This is the point where the graph crosses the y-axis.

From the graph, we can observe the intercepts and fill in the table accordingly.

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

• The axis of symmetry is a vertical line that divides the parabola into two symmetric halves. This line passes through the vertex.

(d) Find the coordinates of the vertex:

• The vertex is the point where the parabola reaches its minimum or maximum value, depending on its orientation.

I will now analyze the image to gather the necessary data. PIL import Image

Load the uploaded image to analyze

image_path = '/mnt/data/1741176019806jyg8a93t.jpg' img = Image.open(image_path)

Display the image to analyze

img.show()I have displayed the image for analysis. Based on the graph, I can now assist you in answering the questions. Here's a breakdown of the answers based on the graph.

1. Does the parabola open upward or downward?

   • The parabola opens upward because it has a "U" shape.

2. Find the intercepts:

   • X-intercepts: From the graph, the parabola intersects the x-axis at approximately $x = -2$ and $x = 2$.
   • Y-intercept: The graph crosses the y-axis at $y = -6$.

3. Find the equation of the axis of symmetry:

   • The axis of symmetry is the vertical line passing through the vertex. From the graph, the axis of symmetry is the line $x = 0$.

4. Find the coordinates of the vertex:

   • The vertex is at $(0, -6)$, where the graph reaches its minimum point.

Please let me know if you'd like any more details or further clarification on the answers!

Here are some related questions to explore further:

1. How can we determine if a quadratic function opens upward or downward without a graph?
2. How can we find the vertex of a parabola given its quadratic equation?
3. What is the significance of the axis of symmetry in a parabola?
4. How do we find the x-intercepts of a parabola algebraically?
5. What does the y-intercept tell us about a quadratic function?

Tip: To determine the axis of symmetry, use the formula $x = -\frac{b}{2a}$ for a quadratic equation $ax^2 + bx + c$.