Question

A parabola has a vertex at (4, 0) and passes through the point (6, 1). Which of the following is the equation of this parabola in the form 2003-18-03-00-00_files/i0230000.jpg?

Answer 1

Easy

y=a(x-h)^2+k
vertex is (h,k)
we know that vertex is (4,0)
input that point for (h,k)
y=a(x-4)^2+0
y=a(x-4)^2
passes thorugh the point (6,1)
input that point to find a
1=a(6-4)^2
1=a(2)^2
1=a(4)
divide both sides by 4
1/4=a

thefor the equation is
y=(1/4)(x-4)^2
or
y=(1/4)x^2-2x+4