https://file.aiquickdraw.com/mathbot/file/1728415968018g06ua1qe.jpg

Let's fill in the table of values for the function \( g(x) = x^2 - 4x \). We will substitute each given value of \( x \) into the function to calculate \( g(x) \).

### Calculations:
1. For \( x = -2 \):
   \[
   g(-2) = (-2)^2 - 4(-2) = 4 + 8 = 12
   \]

2. For \( x = -1 \):
   \[
   g(-1) = (-1)^2 - 4(-1) = 1 + 4 = 5
   \]

3. For \( x = 0 \):
   \[
   g(0) = (0)^2 - 4(0) = 0
   \]

4. For \( x = 2 \):
   \[
   g(2) = (2)^2 - 4(2) = 4 - 8 = -4
   \]

5. For \( x = 4 \):
   \[
   g(4) = (4)^2 - 4(4) = 16 - 16 = 0
   \]

6. For \( x = 5 \):
   \[
   g(5) = (5)^2 - 4(5) = 25 - 20 = 5
   \]

7. For \( x = 6 \):
   \[
   g(6) = (6)^2 - 4(6) = 36 - 24 = 12
   \]

### Completed Table:
| \( x \) | \( g(x) = x^2 - 4x \) |
|:-------:|:---------------------:|
|   -2    |           12          |
|   -1    |           5           |
|    0    |           0           |
|    2    |          -4           |
|    4    |           0           |
|    5    |           5           |
|    6    |           12          |

Would you like assistance with sketching the graph or any further details?

Here are five related questions:
1. How do you determine if a quadratic function opens upward or downward?
2. What are the roots of the function \( g(x) = x^2 - 4x \)?
3. What is the vertex of the parabola for the function \( g(x) = x^2 - 4x \)?
4. How would you find the axis of symmetry for this quadratic function?
5. What is the importance of plotting points when sketching a graph?

**Tip:** The vertex form of a quadratic equation \( ax^2 + bx + c \) helps identify the vertex directly and simplifies graphing.

Sketch the graph of the function by first making a table of values. g(x) = x^2 - 4x

Learn how to graph the quadratic function g(x) = x^2 - 4x by making a table of values and plotting points. This problem involves key algebraic concepts such as quadratic functions, parabolas, and identifying the vertex and axis of symmetry. Suitable for students in Grades 8-10.

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