https://r2.erweima.ai/mathbot/image/1726237223916i0rf7u16.jpg

a.
(-2,-3)


b.
(2,3)


c.
(-3,-2)


d.
(3,2)

The graph in the image is a parabola that opens upward, suggesting that it represents a quadratic function of the form:

\[
y = ax^2 + bx + c
\]

To find which of the provided points (a-d) are part of the parabola, let's first analyze the graph:

1. The vertex of the parabola is at (-1, -3).
2. The graph crosses the x-axis at two points: \(x = -3\) and \(x = 1\), indicating that these are the roots or solutions of the equation.
3. The axis of symmetry is \(x = -1\).

Now, let's analyze the points:

a. **(-2, -3)**: 
   - This point does not lie on the graph, as it does not satisfy the shape of the parabola.

b. **(2, 3)**: 
   - This point does not lie on the graph, as it is far from the trajectory of the curve.

c. **(-3, -2)**:
   - This point is close to the x-axis crossing, but the y-value should be 0 here, not -2.

d. **(3, 2)**: 
   - This point seems incorrect based on the general shape of the parabola as well.

None of the provided points exactly match the parabola's key points. Do you want to continue exploring this problem or clarify something specific? 

Here are 5 follow-up questions:

1. Would you like to calculate the exact equation of this parabola?
2. Do you want help finding other key points on this graph?
3. Shall we analyze the axis of symmetry and vertex further?
4. Are you interested in learning how to plot similar quadratic graphs?
5. Do you want to explore how to solve quadratic equations graphically?

**Tip:** The vertex form of a parabola is often easier to work with when identifying points and characteristics of the graph!

The query submitted by the user:

a. (-2,-3)
b. (2,3)
c. (-3,-2)
d. (3,2)

Explore the properties of a quadratic equation's graph. Determine if points like (-2,-3), (2,3), (-3,-2), and (3,2) are part of the parabola based on the graph and vertex form of the equation. Ideal for students in Grades 8-10 studying quadratic equations.

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