How to find the equation of a parabola with only 3 pts.

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In summary, the conversation discusses finding the equation of a parabola when given three points and the knowledge that the axis of symmetry is parallel to the y-axis. The equation is solved using the general form and standard form of a parabola and the values of a, b, and c are determined using a system of equations. There is also a discussion about a mistake made in solving for b.
  • #1
redretro
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If you have 3 points of a parabola that are'nt the vertex and the only other information you receive is that the A.O.S is parallel to the y-axis how would you acurately find the equation? Everytime I try, I always end up with odd fractions... the pts are (-3,-4),
(-1,-1), (2,3)



2. Homework Equations : general form: y=ax^2+ bx+c standard form: y-h=a(x-k)^2 a=1/4l l is the distance from the vertex to either the directrix or the focus, also that the equations opens either up or down...



Attempt:(-3,-4) -4=9a-3b+c (-1,-1) -1=a-b+c (2,3) 3=4a+2b+c

(-1)(-4=9a-3b-c) (-1)(-4=9a-3b-c)
(-1= a -b+c) (3=4a+2b+c)
+ ___________ +____________
3=-8a+2b 7=-5a+5b


(-5)(3=-8a+2b)
( 2)(7=-5a+5b)
+_____________
1=30a a=1/30

7=-5(1/30)+5b 7= -5/30+5b 215/30=5b 1075/30=b b= 215/6 a=1/30 b=215/6

3=4a+2b+c 3=4/30+2(215/6)+c 86/30= 215/3+c c=-2064/30


after that point: I thought something went wrong and attempted to redo it...-.-
 
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  • #2
I get a = 1/30 also, using determinants to solve the equations for it. I think you're on the right track...
 
  • #3
But in your solution for b, I think there's an issue...

7=-5(1/30)+5b
7= -5/30+5b
215/30=5b
1075/30=b <--- (see the issue?)
b= 215/6
 
  • #4
okay thanks ^.^ I think I understand it more.
 

Related to How to find the equation of a parabola with only 3 pts.

What is a parabola?

A parabola is a type of curved shape that can be seen in many natural and man-made structures, such as the path of a thrown ball or the shape of a satellite dish. It is a conic section, meaning it is formed by the intersection of a plane and a cone.

What are the 3 points needed to find the equation of a parabola?

To find the equation of a parabola, you need to have three points: the vertex, the x-intercept, and one other point on the curve. These points can be given to you or you can find them by plotting the parabola on a graph.

Can I find the equation of a parabola with only 3 points?

Yes, it is possible to find the equation of a parabola with only 3 points. However, it is important to note that the equation will not be unique and there will be infinite possible parabolas that can pass through those 3 points.

What is the standard form of a parabola?

The standard form of a parabola is y = ax^2 + bx + c, where a, b, and c are constants that determine the shape and position of the parabola. This form is useful for graphing and analyzing the properties of the parabola.

Can I use a system of equations to find the equation of a parabola with 3 points?

Yes, a system of equations can be used to find the equation of a parabola with 3 points. You can set up a system of three equations using the given points and solve for the unknown constants a, b, and c. This method is known as the method of elimination.

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