# Homework Help: Finding the equation of a parabola

1. Oct 24, 2005

### Flatland

How do you find the equation of a parabola if you are given it's vertex and 1 point? For example, find the quadratic equation of a parabola that has a vertex of (-2,-2) and goes through the point (-1,0)

2. Oct 24, 2005

### stalefish

General quadratic equation: y=ax^2 + bx + c

Derivative: y' = 2ax + b

At the vertex, the derivate equals to zero. Use this fact and simultaneous equations to arrive at the equation.

Last edited: Oct 24, 2005
3. Oct 24, 2005

### HallsofIvy

More simply, since you are given the vertex of the parabola, you can write the equation y= a(x-x0)2+ y0 where x0 and y0 are the coordinates of the vertex. Choose a to force the parabola to go through the second point.

y= a(x-(-2))2- 2= a(x+2)2- 2. Setting x= -1, y= 0,
0= a(-1+2)2-2= a- 2 so a= 2.

By the way, this is assuming the parabola has a vertical line of symmetry. Otherwise there are an infinite number of parabolas satisfying these conditions.

4. Oct 24, 2005

### ivybond

$$y = 2x^{2}$$
$$y = 2(x+2)^{2} - 2$$