Register to reply

Finding the equation of a parabola

by Flatland
Tags: equation, parabola
Share this thread:
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
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
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.
Oct24-05, 07:26 AM
Sci Advisor
PF Gold
P: 39,363
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.

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