Question

Write an equation for the polynomial function whose graph intercepts the horizontal axis at -7,8,15

Answer 1

The equation for the polynomial function with the given x intercepts would be
`\[ f(x) = k(x + 7)(x - 8)(x - 15) \]`

How to find the equation of the polynomial ?

A polynomial function that intercepts the horizontal axis at the points -7, 8, and 15 can be represented as a product of linear factors corresponding to these x-intercepts.

Given the x-intercepts -7, 8, and 15, the corresponding factors would be (x + 7) , (x - 8) , and (x - 15) . Thus, the polynomial function can be written as:

`\[ f(x) = k(x + 7)(x - 8)(x - 15) \]`

Here, k is a constant that can be any real number. If k is positive, the end behavior of the polynomial will be upwards, and if k is negative, it will be downwards.