Math Problem Statement
Solution
The function modeling the diver's path is given as:
This is a quadratic function of the form , where , , and .
Since is negative, the parabola opens downwards, and the vertex of the parabola represents the maximum point. To find the maximum height, we need to determine the x-coordinate of the vertex using the formula:
Substitute the values of and :
So, the horizontal distance at which the maximum height occurs is .
Now, substitute into the original equation to find the maximum height:
Simplify:
Thus, the maximum height of the diver is 13 feet.
Would you like any more details or have further questions on this? Here are some related questions to consider:
- What is the significance of the vertex in a quadratic function?
- How do you determine whether a parabola opens upwards or downwards?
- How does the discriminant of a quadratic equation relate to its graph?
- What would happen to the maximum height if the coefficients were changed?
- How do you find the axis of symmetry for a quadratic function?
Tip: The vertex formula works for any quadratic function and is a quick way to find the maximum or minimum point depending on the direction of the parabola!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex of a Parabola
Formulas
f(x) = ax^2 + bx + c
Vertex formula: x = -b/2a
Theorems
Maximum height occurs at the vertex of a parabola
Suitable Grade Level
Grades 9-11