Answer:
y = ( x + 3 ) * ( x + 2 ) * ( x - 1 )* 11/60
Step-by-step explanation:
Lets y = f(x) in a cartesian coordinates
Having three zeros:
x = -3 ⇒ x = -2 ⇒ and x = 1
That meas that if x takes the above mentioned values " y " must be zero
therefore y must be of the form
f (x) = y = ( x + 3 ) * ( x + 2 ) * ( x - 1 ) (1)
In that case for y to be zero one of the factors should be zero or
y = 0 x + 3 = 0 and x = - 3 is a zero of the function y .
The same reasoning applies for the other two roots
Now we have to evaluate the other condition.
According to problem statement the function passes through the point ( 3, 11 ) , that means that when x = 3 , y have to be 11, therefore we plug in equation (1) that value to see what happens
y = ( x + 3 ) * ( x + 2 ) * ( x - 1 )
11 = ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1) = 6*5*2 = 60
Then we adjust the expression (1) to meet the condition of the function passing through point ( 3 , 11) as:
y = ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1) * 11/60 (2)
and check to see if we did right
for y to be zero x can be x = - 3 x = -2 and x = 1 in all these cases y = 0. And if x = 3 in equation (2) y = 11. And that what we want to shown. Then the solution is:
y = ( x + 3 ) * ( x + 2 ) * ( x - 1 )* 11/60
