• May 2nd 2010, 09:28 PM
mamajen
ok this is my lasst question of the night i promise!

Find the unique quadratic function that passes through the points (-2, 5), (1,-1), and (6, 29). use matrices to solve
• May 2nd 2010, 09:31 PM
pickslides
Quote:

Originally Posted by mamajen
ok this is my lasst question of the night i promise!

Find the unique quadratic function that passes through the points (-2, 5), (1,-1), and (6, 29). use matrices to solve

You need to create a sytem of equations given these 3 points.

Use $\displaystyle y =ax^2+bx+c$

Here's the first one $\displaystyle (-2,5) \implies 5 = a(-2)^2+b(-2)+c = 4a-2b+c$

You do the next 2, I will then show you the next step.
• May 2nd 2010, 09:40 PM
mamajen
Quote:

Originally Posted by pickslides
You need to create a sytem of equations given these 3 points.

Use $\displaystyle y =ax^2+bx+c$

Here's the first one $\displaystyle (-2,5) \implies 5 = a(-2)^2+b(-2)+c = 4a-2b+c$

You do the next 2, I will then show you the next step.

ok here is what i have.....
(1, -1) -1=a+b+c
(6, 29) 29=36a+6b+c
• May 2nd 2010, 09:55 PM
pickslides
Quote:

Originally Posted by mamajen
ok here is what i have.....
(1, -1) -1=a+b+c
(6, 29) 29=36a+6b+c

so we have,

$\displaystyle -1=a+b+c$
$\displaystyle 29=36a+6b+c$
$\displaystyle 5 = 4a-2b+c$

Which can be written in matrix form as

$\displaystyle \left[ \begin{array}{c} a\\ b\\ c\end{array}\right]=\left[ \begin{array}{ccc} 1 & 1 & 1 \\ 36 & 6 & 1 \\ 4 & -2 & 1 \end{array} \right]^{-1} \left[ \begin{array}{c} -1\\ 29\\ 5\end{array}\right]$

Now you need to find the inverse of a $\displaystyle 3\times 3$ matrix, will be tricky
• May 2nd 2010, 10:04 PM
mamajen
Quote:

Originally Posted by pickslides
so we have,

$\displaystyle -1=a+b+c$
$\displaystyle 29=36a+6b+c$
$\displaystyle 5 = 4a-2b+c$

Which can be written in matrix form as

$\displaystyle \left[ \begin{array}{c} a\\ b\\ c\end{array}\right]=\left[ \begin{array}{ccc} 1 & 1 & 1 \\ 36 & 6 & 1 \\ 4 & -2 & 1 \end{array} \right]^{-1} \left[ \begin{array}{c} -1\\ 29\\ 5\end{array}\right]$

Now you need to find the inverse of a $\displaystyle 3\times 3$ matrix, will be tricky

1, -1, 1

thanks so much for your help!