math
posted by eve on .
Hello. Please, help me solve this:
Parabola y = ax^2 + bx + c passes through the point (2;6). Find the values of a, b and c, if vertex of parabola is (4;10).

let's find the equation in its standard form using the given information
since the vertex is (4,10)
it must be
y = a(x4)^2 10
but (2,6) lies on it
6 = a(2)^2  10
4 = 4a
a = 1
so y = (x4)^2  10
y = x^2  8x + 16  10
y = x^2  8x + 6
so a=1, b=8 and c=6