Question

write an equation for a polynomial function whose graph intersects the horizontal axis at -7, 8, and 15.

Explanation:

Step1: Recall the Factor Theorem

If a polynomial function \( f(x) \) has a root (intercepts the horizontal axis) at \( x = a \), then \( (x - a) \) is a factor of \( f(x) \).

Step2: Identify the factors

The graph intersects the horizontal axis at \( x=-7 \), \( x = 8 \), and \( x = 15 \). So the factors are \( (x - (-7))=(x + 7) \), \( (x - 8) \), and \( (x - 15) \).

Step3: Form the polynomial

A polynomial with these roots can be written as the product of these factors. Let the polynomial be \( f(x) \), then \( f(x)=(x + 7)(x - 8)(x - 15) \). We can also multiply by a non - zero constant \( a \) (usually we can take \( a = 1 \) if not specified otherwise).

Answer:

\( f(x)=(x + 7)(x - 8)(x - 15) \) (or \( f(x)=a(x + 7)(x - 8)(x - 15) \) where \( a
eq0 \))