https://file.aiquickdraw.com/mathbot/file/17261522438125s4mmiuf.jpg

The graph provided shows a parabola, and the question seems to be asking for which of the given points lies on this curve. To determine the correct answer, we can check which of the provided points satisfies the equation of the parabola.

From observation, the parabola has its vertex at \((4, 0)\) and opens downwards. This suggests the general form of the parabola is:

\[
y = a(x - 4)^2 + 0
\]

Since the parabola opens downward, \(a\) will be negative. Next, we will check which of the provided points satisfies the curve. The choices are:

A. (6, -4)  
B. (5, -2)  
C. (3, -1)  
D. (4, 0)  
E. (1, -7)

We can visually verify that the point \( (4, 0) \) lies on the graph, which corresponds to option **D**. This is the vertex of the parabola.

Would you like to see the detailed calculations or explanations? 

Here are five related questions for further exploration:
1. What is the equation of the parabola shown in the graph?
2. How can you determine the direction in which a parabola opens?
3. How can you calculate the vertex of a parabola given its equation?
4. What are the key properties of parabolas in general?
5. How do you find the x-intercepts and y-intercepts of a parabola?

**Tip**: To quickly identify points on a graph, substitute the coordinates of the points into the equation of the graph and see if they satisfy the equation.

Which of the given points lies on the parabola shown in the graph?

Learn how to identify points that lie on a parabola with a vertex at (4, 0). This problem explores key algebraic concepts such as the vertex form of a parabola and graph interpretation. Suitable for students in Grades 8-10.

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