What is the equation written in vertex form of a parabola with a vertex of (3,6) that passes through point (4,4)?

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                         f(x) = a(x - h)² + k

the vertex is (3, 6)  ⇒   h = 3,  k = 6

so:

      f(x) = a(x - 3)² + 6

The parabola goes through the point (4, 4) ⇒   x=4,  f(x)=4

 4 = a(4 - 3)² + 6

 4 = a(1)² + 6

-6           -6

- 2  = a

It means the equation of the parabola in vertex form:

                                f(x) = -2(x - 3)² + 6

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.