https://file.aiquickdraw.com/mathbot/file/1730142500544pufp18r0.jpg

The quadratic function given is:

\[
y = -0.083(x - 6)^2 + 3
\]

This equation represents the jump height \( y \) (in meters) of a kangaroo as a function of the horizontal distance \( x \) (in meters). 

This function is in vertex form \( y = a(x - h)^2 + k \), where the vertex is at the point \( (h, k) \). In this case:
- \( h = 6 \)
- \( k = 3 \)

Thus, the vertex of this function is at the point \( (6, 3) \).

### Interpretation of the Vertex:
The vertex \( (6, 3) \) represents the maximum height of the kangaroo's jump. Specifically:
- The kangaroo reaches a maximum height of 3 meters.
- This maximum height occurs when the kangaroo is 6 meters horizontally from its starting point.

In practical terms, the vertex represents the peak of the jump. Since the parabola opens downward (indicated by the negative coefficient \(-0.083\)), the vertex is indeed the highest point of the jump.

Would you like more details or have any questions?

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### Related Questions
1. How do you calculate the horizontal distance where the jump height is a certain value?
2. What does the coefficient \(-0.083\) tell us about the shape of the parabola?
3. How would the vertex change if the equation was modified?
4. How do you find the horizontal distance when the jump height is zero?
5. How can this function be used to estimate the jump distance of different animals?

### Tip
In a quadratic function in vertex form \( y = a(x - h)^2 + k \), the sign of \( a \) determines whether the parabola opens upwards (positive) or downwards (negative).

Suppose the quadratic function y = -0.083(x - 6)^2 + 3 modeled the jump height y (in meters) of a kangaroo where x represents the horizontal jump distance (in meters). Explain what the vertex of the quadratic function represents.

Learn how the vertex of the quadratic function y = -0.083(x - 6)^2 + 3 represents the peak of a kangaroo's jump. This problem explores concepts in quadratic functions and vertex form, suitable for students in Grades 9-10.

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