Let's start by calculating the values of [tex]\( y \)[/tex] for each [tex]\( x \)[/tex] in the set [tex]\( x = \{-2, -1, 0, 1, 2\} \)[/tex] for the quadratic function [tex]\( y = -2x^2 \)[/tex].
We can organize our results in a table:
| [tex]\( x \)[/tex] | [tex]\( y = -2x^2 \)[/tex] |
|-----------|-----------------|
| [tex]\( -2 \)[/tex] | [tex]\( -8 \)[/tex] |
| [tex]\( -1 \)[/tex] | [tex]\( -2 \)[/tex] |
| [tex]\( 0 \)[/tex] | [tex]\( 0 \)[/tex] |
| [tex]\( 1 \)[/tex] | [tex]\( -2 \)[/tex] |
| [tex]\( 2 \)[/tex] | [tex]\( -8 \)[/tex] |
Now, we will graph the quadratic function using these values.
1. Plot the Points:
- Plot the point [tex]\((-2, -8)\)[/tex].
- Plot the point [tex]\((-1, -2)\)[/tex].
- Plot the point [tex]\((0, 0)\)[/tex].
- Plot the point [tex]\((1, -2)\)[/tex].
- Plot the point [tex]\((2, -8)\)[/tex].
2. Draw the Curve:
- Since this is a quadratic function, the points will form a parabolic shape when connected.
- Draw a smooth curve through the plotted points, making sure the vertex of the parabola is at the origin [tex]\((0, 0)\)[/tex], and the arms of the parabola open downwards.
Here is the visual representation of the resulting parabola from the table of values:
```plaintext
y
|
8|
6|
4|
2|
0|----------------------------------------------
-2|
-4|
-6|
-8|
```
This completes the process of graphing the quadratic function [tex]\( y = -2x^2 \)[/tex] using the specified values for [tex]\( x \)[/tex] and the corresponding [tex]\( y \)[/tex] values.
