Problems with factorization in regard to defining a polynomial
Following cordinate-points are given to define a function:
(½,o), (-2,0) and (1,-3) with the parable roots being ½ and -2. Since d>0, I used the formula: f(x)= a(x-r1)(x-r2), where r1= first root and r2= second root.
So this is what I end up with:
f(x) = a(x-½)(x+2) <=> f(x)= a(x^2+ 2x- ½x- 1) <=> f(x)= ax^2+ 1½x-1
Then I isolate a, by inserting the x and y values of the third coordinate-point (1,-3) and I get:
-3= a(1-0.5)(1+2) <=> -3= a(1+2-0.5-1) <=> -3= a(1.5) <=> -3/1.5 = a <=> a= -2
So the final definition of the function is:
f(x) = -2ax^2 + 1½x - 1
But in the answer list in my text-book, it says the definition should be:
f(x)= 2x^2 + 3x- 2
Can someone please explain to me where I went wrong?
Thank you in advance.