https://file.aiquickdraw.com/mathbot/file/1729808168179yg5368ev.jpg

The equation provided is:

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

You are asked to plot five points on the graph of this function: one point for \( x = 0 \), two points for negative \( x \)-values, and two points for positive \( x \)-values.

### Step-by-step process to find points:

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

2. **For negative values of \( x \):**
   - Let \( x = -2 \):
     \[
     y = \frac{3}{2} (-2)^3 = \frac{3}{2} (-8) = -12
     \]
     So, the point is \( (-2, -12) \).
   
   - Let \( x = -1 \):
     \[
     y = \frac{3}{2} (-1)^3 = \frac{3}{2} (-1) = -\frac{3}{2} \approx -1.5
     \]
     So, the point is \( (-1, -1.5) \).

3. **For positive values of \( x \):**
   - Let \( x = 1 \):
     \[
     y = \frac{3}{2} (1)^3 = \frac{3}{2} = 1.5
     \]
     So, the point is \( (1, 1.5) \).
   
   - Let \( x = 2 \):
     \[
     y = \frac{3}{2} (2)^3 = \frac{3}{2} (8) = 12
     \]
     So, the point is \( (2, 12) \).

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

Plot these points on the graph. The graph should resemble a cubic curve with increasing steepness as \( |x| \) increases.

Would you like any additional explanations or have questions on how to interpret the graph?

Here are five related questions:
1. How does the coefficient \(\frac{3}{2}\) affect the shape of the cubic graph?
2. What would happen to the graph if the exponent of \( x \) was even instead of odd?
3. How can we find the slope at specific points on a cubic function?
4. How do negative values of \( x \) affect the function \( y = \frac{3}{2} x^3 \)?
5. How do you graph transformations of the form \( y = a(x - h)^3 + k \)?

**Tip:** Cubic functions like \( y = \frac{3}{2}x^3 \) always pass through the origin, and their graphs exhibit symmetry about the origin, called *odd symmetry*.

Graph the function y = (3/2)x^3 and 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 key points, including one at x = 0, two at negative x-values, and two at positive x-values. This solution explains the step-by-step process to find these points and visualize the curve.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation