How can you find in a simple way the formula of Parabola that passes

through the point $\displaystyle p(2,1)$ and passes through the points of intersection

of functions $\displaystyle y = x^2 + 3x + 7$ & $\displaystyle y = -2x^2 + x + 10$

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- Apr 28th 2009, 10:14 PMrazemsoft21Formula of Parabola = ??
How can you find in a simple way the formula of Parabola that passes

through the point $\displaystyle p(2,1)$ and passes through the points of intersection

of functions $\displaystyle y = x^2 + 3x + 7$ & $\displaystyle y = -2x^2 + x + 10$ - Apr 28th 2009, 10:27 PMmr fantastic
- Apr 29th 2009, 06:36 AMrazemsoft21
sorry, the 2 equation are:

$\displaystyle y = x^2 + 3x + 7$

$\displaystyle y = -2x^2 + x + 10$

to get points of intersection:

$\displaystyle x^2 + 3x + 7$ = $\displaystyle -2x^2 + x + 10$

$\displaystyle 3x^2 + 2x - 3 = 0$

solving for x = $\displaystyle \frac{-1 \pm \sqrt{10}}{3}$

we find y for each x, and use the 2 points with the third (2 , 1) to solve for A, B, and C in:

$\displaystyle f(x) = Ax^2 + Bx +C$

but the question says use a simple way to find the function !!!

is this a simple way ??