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!