Step 1	The vertex of the parabola is at (-1, 4) so h = -1 and k = 4. Since (2, 1) is a point on the graph of the parabola, let x = 2 and y = 1. Substitute these values into the vertex form of the equation and solve for a.
Show Me	y = a(x - h)^2 + k \quad \quad Vertex Form. 1 = a[2 - (-1)]^2 + 4 \quad \quad \quad Substitute 1 for y, 2 for x, -1 for h, and 4 for k.

Step 2	Simplify the expression .
Show Me	1 = a(9) + 4

Step 3	Subtract 4 from each side .
Show Me	-3 = 9a

Step 4	Divide each side by 9 .
Show Me	-\frac{1}{3} = a

Step 5	Write the equation in vertex form.
Show Me	y = -\frac{1}{3}(x + 1)^2 + 4

Step 6	Check. A graph of \quad y = -\frac{1}{3}(x + 1)^2 + 4 \quad verifies that the parabola passes through the point (2, 1).
Show Me	Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)