Use a system of equations to find the parabola of the form y=ax2+bx+c that goes through the three points given. (2,2), (-4,50), (3,8) y=?

 We must form the system of equations. We will do that by replacing variables  and  in equation of parabola  with coordinates of the given points. Thus, we get system of 3 equations with 3 unknowns  and 

There are several ways to solve this system of equations. We will use Gaussian elimination.

Subtract first equations from the second and then from the third.

Add third equation multiplied...

 We must form the system of equations. We will do that by replacing variables  and  in equation of parabola  with coordinates of the given points. Thus, we get system of 3 equations with 3 unknowns  and 

There are several ways to solve this system of equations. We will use Gaussian elimination.

Subtract first equations from the second and then from the third.

Add third equation multiplied by 6 to the second equation.

Now we solve second equation, then third and then first.

Now we use the value of  to solve the third equation.

Now we use values of  and  to solve the first equation.

Now that we know values of all three parameters  and  we can write the equation of parabola.

         

Graph of the parabola can be seen in the image below.