Question 112971
one form of the equation for a parabola is y=a(x-h)^2+k


this is a parabola with the vertex (nose) at (h,k)


changing the h value moves the parabola horizontally; and changing the k value moves the parabola vertically


the a value determines the width (fat or pointy) of the parabola and the direction of the opening (up or down)


so y=x^2 is parabola with the vertex at the origin (0,0)opening upward


y=(x-2)^2  (y=x^2-4x+4) is a parabola with the vertex at (2,0)


y=(x-2)^2+3  (y=x^2-4x+7) has the vertex at (2,3)