Finding the equation of a parabola without zeros

Question

Hi, I'm being asked to determine equation of a parabola without the zeros

I'm not too sure what that means to be honest,

But, lets say you get 3 points of a parabola, none of them are "zeros", can you determine the equation of the parabola? From just 3 points on a graph?

Answer 1

An equation of a parabola is y = Ax²+Bx+C

 

Let's say that the points (1,3), (-1,-3), and (2,9) are on the graph.

 

Then, we get the system of equations, A + B + C = 3

                                                       A - B + C = -3

                                                     4A + 2B + C = 9

 

Subtract equation 2 from equation 1 to get 2B = 6.  So, B = 3

 

Replace B by 3 in the first equation to get A + C = 0.  So, A = -C

 

The third equation can now be rewritten as 4A + 6 - A = 9

 

                                                                       3A = 3  So, A = 1

                                                                                       C = -1

The parabola has equation y = x² + 3x - 1.  

 

 

                                                  

                                                       

Answer 2

First, zeros mean where the parabola hits the x axis. They're also called roots. They're also called solutions to the equation of the parabola. 

 

Consider the standard form of a parabola

 

y = Ax² + Bx + C

 

If you're given three points and you plug each into this equation, you will get a system of three equations with three unknowns, the unknowns being A, B, and C. 

 

So try that, it ought to work. When you figure out what A, B, and C are, come back to that equation and replace A, B, and C with those numbers.