Finding the equation of a parabola

by Flatland
Tags: equation, parabola
Flatland is offline
Oct24-05, 12:03 AM
P: 150
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)
Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
stalefish is offline
Oct24-05, 01:33 AM
P: 8
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.
HallsofIvy is offline
Oct24-05, 07:26 AM
Sci Advisor
PF Gold
P: 38,894
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.

ivybond is offline
Oct24-05, 11:40 PM
P: 37

Finding the equation of a parabola

Quote Quote by HallsofIvy
... assuming the parabola has a vertical line of symmetry...
Graph first, and you may find a shortcut for a given specific data.
If a point on a parabola is 1 to the right and 2 up from its vertex, it must be parabola
[tex]y = 2x^{2}[/tex]
shifted horizontally and vertically, so its vertex (0,0) moves into (-2,-2), i.e. 2 to the left and 2 down:
[tex]y = 2(x+2)^{2} - 2[/tex]

Register to reply

Related Discussions
finding an equation of a parabola given three points. Precalculus Mathematics Homework 16
Finding a Parabola using three points, no equations Linear & Abstract Algebra 2
Finding the equation of a parabola General Math 3
finding equation of a parabola? Help Precalculus Mathematics Homework 4
Finding the vertex of a parabola from an equation General Math 7