Final answer:
Using the information given, Jeremy's throw can be represented by the quadratic function f(x) = -5x^2 + 30x + 5, which takes into account the initial height of 5 feet and the vertex at (30 feet, 20 feet). The correct answer is option D) f(x) = -5x^2 + 30x + 5.
Step-by-step explanation:
To find the correct quadratic function to represent Jeremy's rock throw, we need to use the given information about the rock's path. We are told the rock is thrown from a height of 5 feet above the water and it reaches its highest point at a horizontal distance of 30 feet from Jeremy's hand and 20 feet above the water. We can use this information to determine the correct coefficients for a quadratic function in the form of f(x) = ax^2 + bx + c.
Since the rock reaches its highest point at a horizontal distance of 30 feet, this point is the vertex of the parabola. The vertex form of a parabola is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex. For this problem, h is 30 and k is 20. In addition, the initial height from which the rock is thrown serves as the y-intercept, which is the constant c in the standard form equation.
The correct function must have a negative leading coefficient because the parabola opens downwards (it is a downwards-facing curve since the rock goes up and then comes down). It must also fit the points (0, 5) as the initial position and (30, 20) as the vertex. Matching these conditions, the correct function is f(x) = -5x^2 + 30x + 5.