How do I find the equation for a parabola?

How do I find the equation for a parabola using a graph, and with coordinates already plotted.

If it makes any difference, its the parabola that goes from up to down, with the maximum value.

railbuff2010-01-04T17:28:25Z

Favorite Answer

y = a(x - p)^2 + q

a is the "stretch" - a>0 ==> parabola opens upwards and has a minimum, a < 0 ==> parabola opens downward and has a maximum. Either of these occur at the vertex, which is (p,q).
The axis of symmetry is vertical and passes through the vertex - it's equation is x = p

Graph the vertex: (p,q)
Draw in the axis of symmetry: x = p

Find a point using a value of x other than p. find y
Graph the point (x,y)
Repeat until you are comfortable with the shape of the graph
Connect the dots with a smooth line.

goober2010-01-04T17:27:20Z

The general form is y = ax^2 + bx + c

You need to find the values for a b and c

So you will need the coordinates for three points. Plug the x and y values into the general equation and then get an equation in a b and c for each point.

Solve these three equations for a b and c.