Parabolas

[steelergirl]

My class is just starting to learn about parabolas and I am having trouble with the following question. I am in eighth grade and my teacher believes in giving us problems that challenge us but with little direction sometimes.

Find the equation of the parabola that passes through the points (1,2), (0,1) and (-1, -2).

When I was trying to figure it out I came up with y= -x^2 - 2x + 1

 

[daon]

System of equations. Do you know how to solve these?

A parabola is given by:

\(\displaystyle y = ax^2 + bx + c\)

Given the three points you can see:

\(\displaystyle 2 = a(1)^2 + b(1) + c\\-2 = a(-1)^2 + b(-1) + c\\1 = a(0)^2 + b(0) + c\)

You can difer from this that c = 1. Thus,

\(\displaystyle 2 = a + b + 1\\-2 = a - b + 1\)

Can you take it from here?