Sure, let's build a table of values for the quadratic function [tex]\( y = -2x^2 \)[/tex] using the given [tex]\( x \)[/tex] values and then graph the function.
### Step-by-Step Solution
1. Identify the given [tex]\( x \)[/tex] values:
[tex]\[
x = \{ -2, -1, 0, 1, 2 \}
\][/tex]
2. Calculate the corresponding [tex]\( y \)[/tex] values using the function [tex]\( y = -2x^2 \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -2(-2)^2 = -2(4) = -8
\][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -2(-1)^2 = -2(1) = -2
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -2(0)^2 = -2(0) = 0
\][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -2(1)^2 = -2(1) = -2
\][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -2(2)^2 = -2(4) = -8
\][/tex]
3. Construct the table of values:
[tex]\[
\begin{array}{c|c}
x & y = -2x^2 \\
\hline
-2 & -8 \\
-1 & -2 \\
0 & 0 \\
1 & -2 \\
2 & -8 \\
\end{array}
\][/tex]
4. Plot these points on a coordinate system:
- [tex]\((-2, -8)\)[/tex]
- [tex]\((-1, -2)\)[/tex]
- [tex]\((0, 0)\)[/tex]
- [tex]\((1, -2)\)[/tex]
- [tex]\((2, -8)\)[/tex]
5. Draw the quadratic curve:
- Plot the points on the coordinate plane.
- Draw a smooth, continuous curve passing through all the plotted points.
The graph will be a downward-opening parabola since the coefficient of [tex]\( x^2 \)[/tex] is negative.
This table and graph represent the function [tex]\( y = -2x^2 \)[/tex] with the specified [tex]\( x \)[/tex] values.
