https://file.aiquickdraw.com/mathbot/file/1726103065675fxbelf5o.jpg

The problem in the image asks to **graph the function**:

\[
y = \frac{3}{2}x^3
\]

It also instructs you to plot **five points** on the graph:
1. **One point at \(x = 0\)**.
2. **Two points with negative \(x\)-values**.
3. **Two points with positive \(x\)-values**.

### Step-by-Step Solution:

The given function is a cubic function, which means its graph will resemble an "S" curve. Let's calculate the required points.

#### 1. For \(x = 0\):
\[
y = \frac{3}{2} \cdot 0^3 = 0
\]
So, the point is \((0, 0)\).

#### 2. For negative \(x\)-values (e.g., \(x = -2\) and \(x = -1\)):
\[
y = \frac{3}{2} \cdot (-2)^3 = \frac{3}{2} \cdot (-8) = -12
\]
So, the point is \((-2, -12)\).

\[
y = \frac{3}{2} \cdot (-1)^3 = \frac{3}{2} \cdot (-1) = -\frac{3}{2} = -1.5
\]
So, the point is \((-1, -1.5)\).

#### 3. For positive \(x\)-values (e.g., \(x = 1\) and \(x = 2\)):
\[
y = \frac{3}{2} \cdot 1^3 = \frac{3}{2} \cdot 1 = 1.5
\]
So, the point is \((1, 1.5)\).

\[
y = \frac{3}{2} \cdot 2^3 = \frac{3}{2} \cdot 8 = 12
\]
So, the point is \((2, 12)\).

### Summary of Points:
- \((0, 0)\)
- \((-2, -12)\)
- \((-1, -1.5)\)
- \((1, 1.5)\)
- \((2, 12)\)

Now you can plot these points on the graph provided.

---

Would you like further details or have any other questions?

Here are 5 follow-up questions you might explore:
1. How does changing the coefficient of \(x^3\) affect the shape of the graph?
2. What is the general shape of a cubic function like \(y = ax^3\)?
3. How would the graph change if the power of \(x\) were even instead of odd?
4. Can you identify the end behavior of this cubic function as \(x\) approaches \(\infty\) and \(-\infty\)?
5. What would happen to the graph if a constant term was added to the function \(y = \frac{3}{2}x^3 + C\)?

**Tip:** For cubic functions, the graph always has one inflection point where the curve changes concavity.

Graph the function y = (3/2)x^3. Plot five points on the graph: one point with x = 0, two points with negative x-values, and two points with positive x-values.

Learn how to graph the cubic function y = (3/2)x^3 by plotting five points, including one at x = 0, two with negative x-values, and two with positive x-values. Understand the key characteristics of cubic functions, suitable for students in Grades 9-12.

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