Question

Graph the function. y=2x2

Answer 1

To graph the function \( y = 2x^2 \), we can follow these steps:

1. **Identify the Shape**: The function \( y = 2x^2 \) is a quadratic function, which means its graph will be a parabola opening upwards since the coefficient of \( x^2 \) (which is 2) is positive.

2. **Vertex**: The vertex of the parabola in this case is at the origin (0, 0) because there are no additional constants added to the equation.

3. **Plot Key Points**: To graph the parabola, we can calculate some key points:
- When \( x = -2 \):
\[
y = 2(-2)^2 = 2(4) = 8 \quad \Rightarrow \quad (-2, 8)
\]
- When \( x = -1 \):
\[
y = 2(-1)^2 = 2(1) = 2 \quad \Rightarrow \quad (-1, 2)
\]
- When \( x = 0 \):
\[
y = 2(0)^2 = 0 \quad \Rightarrow \quad (0, 0)
\]
- When \( x = 1 \):
\[
y = 2(1)^2 = 2(1) = 2 \quad \Rightarrow \quad (1, 2)
\]
- When \( x = 2 \):
\[
y = 2(2)^2 = 2(4) = 8 \quad \Rightarrow \quad (2, 8)
\]

4. **Symmetry**: The graph will be symmetric about the y-axis since the function is even (only even powers of x).

5. **Scale**: Choose an appropriate scale for both axes. You can set the x-axis to go from -3 to 3 and the y-axis from -1 to 9 for better visualization.

6. **Drawing the Graph**: Plot the points above on a graph and then connect them with a smooth curve.

The final shape should look like a "U"-shaped curve opening upward with the vertex at the origin, and points (-2, 8), (-1, 2), (1, 2), and (2, 8) all lying on the curve.

In a text format, the graph would look like this:

```
|
8 | * *
7 |
6 |
5 |
4 |
3 |
2 | * *
1 |
0 |___________________________
-3 -2 -1 0 1 2 3
```

This illustrates the general shape of the parabola defined by the equation \( y = 2x^2 \). You can use graphing software or a graphing calculator for a more accurate and visually appealing representation.