Question

Write an equation for the parabola whose vertex is at (3,3) and which passes through (5,27).

Answer 1

General Equation:
\[p(x) = a(x-h)^2 + k\]
the vertex is the point (h, k).

let's plug that in:\[p(x) = a(x-3)^2 + 3\]
all we need now is a.
you're told that the point (5, 27) exists, let's plug that in:

\[27 = a(5-3)^2 + 3\]

solve for a.

you're parabola general equation would be:

\[p(x) = A(x-3)^2 + 3\]

where A is whatever "a" is [an actual number]

Answer 2

Thank you soo much!

Answer 3

glad i could help :)

let me know if you want me to double check your final answer