Find the equation of the parabolay=ax² +bx+cthat contains the points (1, -2), (2, 0), and (4, 22).

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- May 10th 2009, 11:33 AMbearej50Equation of a ParabolaFind the equation of the parabola
*y*=*ax*² +*bx*+*c*that contains the points (1, -2), (2, 0), and (4, 22).

- May 10th 2009, 11:36 AMMush
Plug in the points and you'll get three equations.

$\displaystyle a+b+c = -2$

$\displaystyle 4a+2b+c = 0 $

$\displaystyle 16a+4b + c = 22 $

You can solve this system of equations in a number of ways. I recommend setting up a matrix.

$\displaystyle \bigg(\begin{array}{ccc}

1 & 1 & 1 \\

4 & 2 & 1 \\

16 & 4 & 1 \end{array}\bigg) \bigg( \begin{array}{ccc}

a \\

b \\

c \end{array}\bigg) = \bigg(\begin{array}{ccc}

-2 \\

0 \\

22 \end{array} \bigg)$

So let's write that as $\displaystyle AX = B $. We want to find x, hence: $\displaystyle X = BA^{-1} $

And you know how to calculate the inverse of a 3x3 matrix hopefully! $\displaystyle A^{-1} = \frac{adj(A)}{det(A)} $ - May 10th 2009, 12:18 PMbearej50
I was taught a different way. Subtract the equations from one another.

I got a = 13/5, b = -23/5, and c = 0. Is this right? - May 10th 2009, 12:24 PMMush