Hi, i cant figure out how to set up this question:

ax^2 + bx + c passes through (-1,5) and has a horizontal tangent at (1,7) find the coefficents a b and c

Thanks.

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- May 11th 2010, 06:15 PMAriModelling a quadratic - Systems of linear equations
Hi, i cant figure out how to set up this question:

ax^2 + bx + c passes through (-1,5) and has a horizontal tangent at (1,7) find the coefficents a b and c

Thanks. - May 11th 2010, 06:23 PMdwsmith
- May 11th 2010, 06:26 PMAri
k im confused, how does that help me find the the values for a,b,c?

edit: and can you please explain how you got that? i feel very confused atm lol. - May 11th 2010, 06:29 PMdwsmith
Setup the coefficient matrix for the two equations and solve simultaneously.

- May 11th 2010, 06:34 PMAri
- May 11th 2010, 06:35 PMdwsmith
- May 11th 2010, 06:36 PMAri
- May 11th 2010, 06:38 PMdwsmith
- May 11th 2010, 06:41 PMAri
is the answer just going to be a,b,c in parametric form or will there be coefficent values, if so how do i get values for them?

- May 11th 2010, 06:43 PMdwsmith
- May 11th 2010, 06:46 PMAri
- May 11th 2010, 06:48 PMdwsmith
$\displaystyle \begin{bmatrix}

1 & -1 & 1 & 5\\

0 & 1 & 2 & 10

\end{bmatrix}\rightarrow \begin{bmatrix}

1 & 0 & 3 & 15\\

0 & 1 & 2 & 10

\end{bmatrix}$ - May 11th 2010, 06:49 PMAri
- May 11th 2010, 06:52 PMdwsmith
Yes you can right your solution as you would the nullity with a free variable.

Note: Not all under determined linear systems are consistent. - May 11th 2010, 06:54 PMAri