algebra
posted by Lee on .
what is the equation in standard form of a parabola that contain the following points?
(2,20),(0,4),(4,20)
Please Help

you can probably save some time by looking at the points. You know that parabolas are symmetric, so, since y(2) = y(4), the axis of symmetry is at x=(2+4)/2 = 1.
So, with x=1 the axis of symmetry (and hence at the vertex), you will have
y = a(x1)^2+k
at x=0, y= 4, so
4 = a+k
20 = 9a + k
k=2
a=2
so, y = 2(x1)^2  2
or, y = 2x^2 + 4x  4

or, if you let y = ax^2 + bx + c,
20 = 4a  2b + c
4 = c
20 = 16a + 4b + c
a = 2
b = 4
c = 4
y = 2x^2 + 4x  4 
Thanks for helping I have posted two other questions if you might be able to help