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The function given is:

\[
h(x) = -0.03(x - 14)^2 + 6
\]

This function models the jump of a red kangaroo, where \( x \) is the horizontal distance traveled (in feet), and \( h(x) \) is the height (in feet). The problem states that when the kangaroo jumps from a higher location, it lands 5 feet farther away.

To find a function that models the second jump, we need to adjust the \( x \)-value for the distance by 5 feet. Since the maximum distance occurs at \( x = 14 \) for the first function, adding 5 feet shifts the entire parabola horizontally to the right by 5 units.

To model the second jump:

1. Shift the vertex 5 feet farther horizontally. 
2. Update the function with the new vertex point at \( x = 19 \) (since \( 14 + 5 = 19 \)).

Thus, the function for the second jump becomes:

\[
h(x) = -0.03(x - 19)^2 + 6
\]

This function represents the kangaroo's jump from a higher location where it lands 5 feet farther.

Would you like more details, or do you have any questions?

Here are some related questions you might be interested in:

1. How does shifting a parabola horizontally affect its vertex form equation?
2. What is the significance of the coefficient of \( (x - h)^2 \) in the function \( a(x - h)^2 + k \)?
3. How can we find the maximum height of the kangaroo's jump using the function?
4. What would be the effect on the function if the kangaroo's jump increased in height instead of distance?
5. How do you find the x-intercepts of the function \( h(x) = -0.03(x - 14)^2 + 6 \)?

**Tip:** When dealing with quadratic functions, remember that horizontal shifts directly modify the \( x \)-value in the equation \( (x - h) \), where \( h \) is the horizontal shift.

The function h(x) = -0.03(x - 14)^2 + 6 models the jump of a red kangaroo, where x is the horizontal distance traveled in feet and h(x) is the height in feet. When the kangaroo jumps from a higher location, it lands 5 feet farther away. Write a function that models the second jump. Round values in your equation to the nearest hundredth, if necessary.

Learn how to adjust the quadratic function h(x) = -0.03(x - 14)^2 + 6 to model a red kangaroo's jump from a higher location. This step-by-step solution explains how to shift the parabola horizontally to account for a 5-foot increase in distance.

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