The roots of a polynomial function are -2, -5, and 3. There's a relative minimum at (-3.667, -14.815) and relative maximum at (1,36). What is the equation for the graph?

Answer 1

Hey Ryan!

It is given that the roots are -2, -5, and 3, so we can at least write the function as below:

f(x) = (x+2)(x+5)(x-3)

However, we don't know if this is a positive function or a negative function, so let's check to see if the value (1,36) will come out if we plug in 1 for x:

f(x) = (1+2)(1+5)(1-3)

f(x) = 3*6(-2)

f(x) = -36

This didn't work out, so the function would be negative to get a positive 36, to give you a function as such:

f(x) = -(x+2)(x+5)(x-3)

Answer 2

Since we know the roots can write the equation in factored form y= a(x+2)(x+5)(x-3) Can use either of the given points to calculate a I will use (1,36)

36=a(1+2)(1+5)(1-3)

36= a[(3 (6)(-2)]

36 =-36a so a=-1 therefore equation is y=-(x+2)(x+5)(x-3) If you want to abuse yourself and multiply this out to put in standard form, be my guest. But it is not necessary