Math Problem Statement
Solution
The function given is:
This function models the jump of a red kangaroo, where is the horizontal distance traveled (in feet), and 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 -value for the distance by 5 feet. Since the maximum distance occurs at for the first function, adding 5 feet shifts the entire parabola horizontally to the right by 5 units.
To model the second jump:
- Shift the vertex 5 feet farther horizontally.
- Update the function with the new vertex point at (since ).
Thus, the function for the second jump becomes:
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:
- How does shifting a parabola horizontally affect its vertex form equation?
- What is the significance of the coefficient of in the function ?
- How can we find the maximum height of the kangaroo's jump using the function?
- What would be the effect on the function if the kangaroo's jump increased in height instead of distance?
- How do you find the x-intercepts of the function ?
Tip: When dealing with quadratic functions, remember that horizontal shifts directly modify the -value in the equation , where is the horizontal shift.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Parabola Shifting
Formulas
Quadratic Equation in Vertex Form: h(x) = a(x - h)^2 + k
Theorems
Shifting the Vertex of a Parabola Horizontally
Suitable Grade Level
Grades 9-11