# Find the equation for a parabola given 3 points

Doodledawg

## Homework Statement

Find an equation for a parabola that passes through the following points. To solve you must use triple elimination, you may check you answer any way you wish

## The Attempt at a Solution

okay so the points given were (1,-2) (-3,10) and (4,31)
I got to the point of making equations to olve with but then my brain hit a wall. What do i need to do next?
-2=a+b+c
10=9a -3b +c
and
31= 16a +4b +c

Doodledawg
i really am not good at quadratics

konthelion

## The Attempt at a Solution

okay so the points given were (1,-2) (-3,10) and (4,31)
I got to the point of making equations to olve with but then my brain hit a wall. What do i need to do next?
-2=a+b+c
10=9a -3b +c
and
31= 16a +4b +c

This is a system of linear equations. There are several ways to solve for a,b, and c. One way is to use linear algebra and set up a matrix equation "Ax=b". Where A is the matrix with coefficients, x is vector [a b c] and b is vector [-2 10 31]
$$$\left( \begin{array}{ccc} 1 & 1 & 1 \\ 9 & -3 & 1 \\ 16 & 4 & 1 \end{array} \right)$$$
Now, solve for x

Homework Helper
What you found is now a system of three simultaneous equations in three unknowns (which you've set up correctly), those unknowns being the coefficients of the equation for your parabola. Are you comfortable with solving such systems?

Doodledawg
im not very comforable with them

Doodledawg
okay i got down to b=2a-3
but i don't know where to go from here

Doodledawg
This is a system of linear equations. There are several ways to solve for a,b, and c. One way is to use linear algebra and set up a matrix equation "Ax=b". Where A is the matrix with coefficients, x is vector [a b c] and b is vector [-2 10 31]
$$$\left( \begin{array}{ccc} 1 & 1 & 1 \\ 9 & -3 & 1 \\ 16 & 4 & 1 \end{array} \right)$$$
Now, solve for x
I have to use triple elimination

Doodledawg
okay i got the right answer with the matrices:
y=2x^2+x-5
but how do i find this through triple elimination?

konthelion
okay i got the right answer with the matrices:
y=2x^2+x-5
but how do i find this through triple elimination?
Could you explain what a triple elimination is? I've never heard this term before. Is this another name for Gaussian elimination?

shawshank
no it's the classic way of doing things, we do it in high school.

Ok, so you have 3 equations:

[1]. -2=a + b +c
[2]. 10=9a -3b +c
[3]. 31= 16a +4b +c

Eliminate a by using 9 * [1] - [2] and then 16 * [1] - [3]

(-18 = 9a + 9b + 9c) - (10 = 9a - 3b + c) ---> -28 = 12b + 8c [4]
(-32 = 16a + 16b + 16c) - (31= 16a +4b +c) ---> -63 = 12b + 15c [5]

eq [4] - eq [5], should be left with c now.

Now solve for c

Plug c back into [4]

Solve for b

Now use eq [1], plug back b and c

Solve for a

Doodledawg
yeah ok thx
im actually in high school and feel like a total idiot but thanks for helping me
i much appreciate it