Return to Assignments Quadratic functions and graphs

### Assignment 9

Calculate the equation of the parabola going through the points , and .

### Solution

The general equation of a parabola is:

We have to calculate the values of , and based on the fact that the given points lie on the parabola.

lies on the parabola, thus .

lies on the parabola, thus

lies on the parabola, thus

So we have two solve two linear equations with two variables and :

Multiply the second equation by and subtract the result from the first equation (in this way we eliminate ):

If we substitute this value of in the second equation we get for :