Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola.
Suppose P is a parabola with focus (4,3) and directrix y=1. The point (8,6) is on P because (8,6) is 5 units away from both the focus and the directrix.
If we write the equation whose graph is P in the form y=ax2+bx+c, then what is a+b+c?
+130462 The vertex is ( 4, 2)
We can start with this form
4p ( y - k) = ( x - h)^2 where p = 1 and ( h, k) is the vertex
4p ( y - 2) = ( x - 4)^2
4 ( y - 2) = x^2 - 8x + 16
4y - 8 = x^2 - 8x + 16
4y = x^2 - 8x + 24 divide both sides by 4
y = (1/4)x^2 - 2x + 6
a = (1/4) b = -2 and c = 6
And their sum is 4 + 1/4 = 17 / 4
