Question

Graph the function y=2x^2

Answer 1

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

1. **Identify the shape**: The function \( y = 2x^2 \) is a parabola that opens upwards because the coefficient of \( x^2 \) (which is 2) is positive.

2. **Find the vertex**: The vertex of the parabola is at the origin (0, 0) since there are no linear or constant terms in the equation.

3. **Determine the axis of symmetry**: The axis of symmetry is \( x = 0 \) (the y-axis).

4. **Calculate some key points**: Choose several values for \( x \) to find corresponding \( y \) values:
- \( x = -2 \): \( y = 2(-2)^2 = 8 \)
- \( x = -1 \): \( y = 2(-1)^2 = 2 \)
- \( x = 0 \): \( y = 2(0)^2 = 0 \)
- \( x = 1 \): \( y = 2(1)^2 = 2 \)
- \( x = 2 \): \( y = 2(2)^2 = 8 \)

So the points to plot are: \( (-2, 8) \), \( (-1, 2) \), \( (0, 0) \), \( (1, 2) \), and \( (2, 8) \).

5. **Plot the points**: On a coordinate plane, plot the points found.

6. **Draw the parabola**: Connect the points with a smooth curve to form the parabola.

### Description of the Graph
- The vertex is at (0, 0).
- The parabola is symmetric about the y-axis.
- As \( x \) moves away from 0 in both the positive and negative directions, \( y \) increases.

If you plot this on graphing software or a graphing calculator, you will see the characteristic U-shape of the function \( y = 2x^2 \).