Question

I don't get how to do this. I'm so lost please help me.

Determine the equation of the parabola with roots 2+√3 and 2-√3, and is passing through the point (2,5)

this is what i did but its the wrong answer:

y= a[x + (2+√3)] [x+(2-√3)]
5= a[2 + (2+√3)] [2+(2-√3)]
5= a[ 4+√3] [4-√3]
5= 12.99a
a= 0.38

therefore,y = 0.38[x+(2+√3)][x+(2-√3)]
but this is wrong

Answer 1

If you know a root and form the factors you have to subtract the root.
e.g. if x = 3, then the corresponding factor is (x-3)

so you should have had

y = a[x - (2+√3)][x-(2-√3)]
= a(x-2-√3)(x-2+√3)
= a(x^2 - 4x +1)

now sub in the point (2,5)
5 = a(4 - 8 + 1)
a = -5/3

y = (-5/3)[x^2 - 4x + 1)