Find the standard equation of the parabola with vertical axis, that has vertex (3,-2) and passes through the point (5,4).
Is it y=5/4(x-3)^3-2?
Hi purplec16,
The standard (vertex) form of your parabola is:
$\displaystyle y=a(x-h)^2+k$
(h, k) is your vertex which is (3, -2)
(x, y) is a point on the curve which is (5, 4)
Substitute this information into the vertex equation to solve for a.
$\displaystyle 4=a(5-3)^2-2$
$\displaystyle a=\frac{3}{2}$
Put it all back together again to get:
$\displaystyle y=\frac{3}{2}(x-3)^2-2$