Answer:
f(x) = x^2 + x - 2.
Step-by-step explanation:
We can write it in factor form as follows:
y = a(x - 1)(x + c)
It's x - 1 because 1 is given as a root of the equation and a and c are constants.
Substituting the other given points:
-2 = a(0 - 1)(0 + c)
-ac = -2
ac = 2
Also:
10 = a(3 - 1)(3 + c)
10 = 2a(3 + c)
6a + 2ac = 10
But ac = 2, so:
6a + 4 = 10
6a = 6
a = 1.
ac = 2 so c = 2.
So our equation is f(x) = (x - 1)(x + 2)
or f(x) = x^2 + x - 2.
