https://file.aiquickdraw.com/mathbot/file/1726976499244grizqemh.jpg

The function given in the image is:

\[
g(x) = (x - 10)^2
\]

This is a quadratic function in vertex form, where the general vertex form of a quadratic function is:

\[
y = a(x - h)^2 + k
\]

In this case:
- \( h = 10 \)
- \( k = 0 \)
- \( a = 1 \)

Thus, the graph represents a parabola that opens upwards with its vertex at the point \( (10, 0) \).

### Key points of the graph:
- **Vertex**: \( (10, 0) \)
- **Axis of symmetry**: \( x = 10 \) (vertical line through the vertex)
- **Direction of opening**: Since the coefficient of \( (x - 10)^2 \) is positive, the parabola opens upwards.
- **Intercepts**: 
  - **Y-intercept**: Substitute \( x = 0 \) into the equation \( g(0) = (0 - 10)^2 = 100 \). So the y-intercept is \( (0, 100) \).
  - **X-intercept**: Since the vertex is at \( (10, 0) \), the x-intercept is \( (10, 0) \).

### To graph:
1. Plot the vertex \( (10, 0) \).
2. Sketch a parabola that opens upwards from the vertex.
3. The parabola will be symmetric about the line \( x = 10 \).
4. Include the point \( (0, 100) \) as a guide for the shape of the graph.

Would you like further details on how to graph this manually or using a graphing tool? 

### Related Questions:
1. What is the effect of changing the value of \( h \) in the function \( (x - h)^2 \)?
2. How does changing the value of \( a \) affect the width and direction of the parabola?
3. What are the steps to find the vertex of a quadratic function?
4. How do you determine the axis of symmetry from a quadratic function?
5. What is the significance of the y-intercept in a quadratic function?

### Tip:
Always start by identifying the vertex and axis of symmetry when graphing quadratics in vertex form—it makes the graphing process much easier!

Graph the following function: g(x) = (x - 10)^2

Learn how to graph the quadratic function g(x) = (x - 10)^2, with detailed explanations on key concepts such as vertex form, axis of symmetry, and intercepts. Suitable for students in Grades 8-10.

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