Question

Vertex(2,4), point (1,-2) write the equation of the parabola in vertex form

Answer 1

first off it is going to look like
\[y=a(x-2)^2+4\] replace x by 1, set the result equal to -2 and solve for a

Answer 2

\[y=a(1-2)^2+4=-2\]
\[a+4=-2\]
\[a=-6\]
equation is
\[y=-6(x-2)^2+4\]