# Thread: How to create a quadratic model without graphing calc?

1. ## How to create a quadratic model without graphing calc?

Hello all,

My teacher gave a lesson yesterday on how to create a quadratic model for a list of statistics when given three points on the scatter plot graph. Unfortunately, I wasn't there, and today, I didn't understand it well when she tried to explain it to me.

An example from today's class was,

Use points (0,0)(151,5) and (686,30) to find a quadratic model?

How would I do this, could somebody explain? Thanks!

2. Originally Posted by Kyle
Hello all,

My teacher gave a lesson yesterday on how to create a quadratic model for a list of statistics when given three points on the scatter plot graph. Unfortunately, I wasn't there, and today, I didn't understand it well when she tried to explain it to me.

An example from today's class was,

Use points (0,0)(151,5) and (686,30) to find a quadratic model?

How would I do this, could somebody explain? Thanks!
You could use your 3 points and find 3 equations with 3 variables to substitute back into the general quadratic model $f(x)=ax^2+bx+c$

With (0. 0), (1) $a(0^2)+b(0)+c=0$, c = 0.

With (151, 5), (2) $a(151^2)+b(151)+0=5$

With (686, 30), (3) $a(686^2)+b(686)+0=30$

Solve the system of equations (2) and (3) for a and b. Then plug them back into the general formula for the quadratic. c = 0, so the equation will have only a quadratic term and a linear term.

3. Thanks, but I have one more question.

Because of the fact that one of the points was (0,0), the problem was easier to solve because we were only left with two variables.

How would I solve the problem if another point, (850,40) was given instead of the point mentioned above?

Thanks for all the help!

4. Originally Posted by Kyle
Thanks, but I have one more question.

Because of the fact that one of the points was (0,0), the problem was easier to solve because we were only left with two variables.

How would I solve the problem if another point, (850,40) was given instead of the point mentioned above?

Thanks for all the help!
It's basically the same procedure. You just pick 2 of the equations and eliminate one of the variables. Then you take 2 more and eliminate the same variable. Then, you have a system in 2 variables.

Take a look here: SYSTEMS OF EQUATIONS in THREE VARIABLES

The example uses a circle, but the methodolgy is the same as with a parabola. The example also solves the system using substitution and elimination.