# Finding the equation of a function

#### Paymemoney

Hi

I need help on the following question:

1) The graph of a polynomial function shows x-axis intercepts at x = -1 and x = 3 and touches the x-axis (with a turning-point) at x = 2. The y-axis intercepts is at y = 24. Assuming the polynomial has degree four, write its equation in factorized form.

The equation i got is $$\displaystyle y = (x+1)(x-3)(x-2)^2.$$
This is incorrect, how did the book's answer get $$\displaystyle y = -2(x+1)(x-3)(x-2)^2$$

P.S

Hi

I need help on the following question:

1) The graph of a polynomial function shows x-axis intercepts at x = -1 and x = 3 and touches the x-axis (with a turning-point) at x = 2. The y-axis intercepts is at y = 24. Assuming the polynomial has degree four, write its equation in factorized form.

The equation i got is $$\displaystyle y = (x+1)(x-3)(x-2)^2.$$
This is incorrect, how did the book's answer get $$\displaystyle y = -2(x+1)(x-3)(x-2)^2$$

P.S
hi

the question also assumes that the polynomial has integer coefficient .

so f(x)=a(x+1)(x-3)(x-2)^2

f(0)=24

24=a(0+1)(0-3)(0-2)^2

a=24/(-12)=-2

hence , f(x)=-2(x+1)(x-3)(x-2)^2 as suggested by the answer

Paymemoney