Question

Y=5/4x^3
Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then click on the graph-a-function button.

Answer 1

To plot points on the graph of the function \( y = \frac{5}{4}x^3 \), we will calculate \( y \) values for the specified \( x \) values.

### Points with calculated coordinates

1. **For \( x = 0 \)**:
\[
y = \frac{5}{4} \cdot 0^3 = 0
\]
Point: \( (0, 0) \)

2. **For \( x = -2 \)**:
\[
y = \frac{5}{4} \cdot (-2)^3 = \frac{5}{4} \cdot (-8) = -10
\]
Point: \( (-2, -10) \)

3. **For \( x = -1 \)**:
\[
y = \frac{5}{4} \cdot (-1)^3 = \frac{5}{4} \cdot (-1) = -\frac{5}{4} = -1.25
\]
Point: \( (-1, -1.25) \)

4. **For \( x = 1 \)**:
\[
y = \frac{5}{4} \cdot 1^3 = \frac{5}{4} \cdot 1 = \frac{5}{4} = 1.25
\]
Point: \( (1, 1.25) \)

5. **For \( x = 2 \)**:
\[
y = \frac{5}{4} \cdot 2^3 = \frac{5}{4} \cdot 8 = 10
\]
Point: \( (2, 10) \)

### Summary of Points
Here are the five points we've calculated:
- \( (0, 0) \)
- \( (-2, -10) \)
- \( (-1, -1.25) \)
- \( (1, 1.25) \)
- \( (2, 10) \)

Now, you can plot these points on a graph and then click on the "graph-a-function" button. The graph will show a cubic function, which takes the shape of an "S" tilted to the right. The function increases for positive values of \( x \) and decreases for negative values, demonstrating the nature of cubic polynomials.