SOLUTION: Write a quadratic function with the following features: x-intercept = (-3,0) and (1,0); y-intercept = (0,2).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a quadratic function with the following features: x-intercept = (-3,0) and (1,0); y-intercept = (0,2).      Log On


   

Question 1092310: Write a quadratic function with the following features:
x-intercept = (-3,0) and (1,0); y-intercept = (0,2).
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!

A quadratic polynomial with x-intercepts a and b is of the form
P%28x%29+=+c%28x-a%29%28x-b%29
where c is some constant.

In your problem, with x-intercepts at -3 and 1, the polynomial is
P%28x%29+=+c%28x%2B3%29%28x-1%29

To determine the value of the constant c, use the given information that the y-intercept (which is P(0)) is 2:
c%283%29%28-1%29+=+2
-3c+=+2
c+=+-2%2F3

And the complete polynomial (in factored form) is
P%28x%29+=+%28-2%2F3%29%28x%2B3%29%28x-1%29