Question

Write the equation of the parabola that has a vertex at (4,6) and passes through (5,8)

Answer 1

A parabola has vertex at (4,6) and passes through the point (5,8).

The general equation of the parabola is:

$y=a(x-h)^2+k$

Where (h,k)=(4,6) in this case so it follows:

$y=a(x-4)^2+6$

Also it passes through (5,8) so it follows:

$\begin{gathered} 8=a(5-4)^2+6 \\ a=2 \end{gathered}$

Hence the equation is:

$y=2(x-4)^2+6$