Final answer:
Due to an error in the provided function for the football's path, we cannot solve for the horizontal distance the football travels. The accurate calculation would involve solving the quadratic formula for f(x) = 0, but with the given equation, this cannot be done accurately.
Step-by-step explanation:
The question asks to determine how far a football travels after being kicked, based on a provided quadratic function that models the football's path. The function given is f(x) = -169 (x – 65)^2 + 25. To find the total horizontal distance the football travels, we need to look for the points where the football's height, f(x), would be zero, which corresponds to the football hitting the ground.
When f(x) = 0, the equation becomes 0 = -169 (x – 65)^2 + 25. However, we can see that there's an error in the function since there's no 'x' to solve for in the equation. Typically, to find the horizontal distance, we would solve the quadratic equation for the values of 'x' that make the equation equal to zero. In this case, it seems there's a typo. Assuming a correct function to be something like f(x) = -169x^2 + 65x + 25, we'd solve for the roots where the football hits the ground (f(x) = 0), but with insufficient information, we cannot conclude the correct answer between the given options of 169 feet, 130 feet, 30 feet, or 25 feet.