grade 11 math
posted by priya on .
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

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 (x3)
so you should have had
y = a[x  (2+√3)][x(2√3)]
= a(x2√3)(x2+√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)