Final answer:
The correct equation for a polynomial function that intercepts the horizontal axis at -7, 8, 15 is f(x) = (x + 7)(x - 8)(x - 15).
Step-by-step explanation:
The question asks for the equation of a polynomial function whose graph intercepts the horizontal axis at -7, 8, 15. To find the polynomial equation, we need to transform the x-intercepts into factors of the polynomial. For the graph of a polynomial to intercept the horizontal axis at a certain x-value, that x-value must be a root of the polynomial, meaning that the polynomial can be factored to have a term of the form (x - r) where r is a root. Therefore, if we have roots at -7, 8, and 15, the factors of the polynomial are (x + 7), (x - 8), and (x - 15), respectively. Multiplying these factors gives us the polynomial in expanded form.
The correct equation for a polynomial function that meets the given conditions is:
f(x) = (x + 7)(x - 8)(x - 15)