# Formula of Parabola = ??

• Apr 28th 2009, 10:14 PM
razemsoft21
Formula 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 PM
mr fantastic
Quote:

Originally Posted by razemsoft21
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 $\displaystyle y = x^2 + 3x + 7$ & $\displaystyle y = -2x + x + 9$

Step 1: Solve the following equations simultaneously:

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

$\displaystyle y = -2x + x + 9$

Can you do this?
• Apr 29th 2009, 06:36 AM
razemsoft21
Quote:

Originally Posted by mr fantastic
Step 1: Solve the following equations simultaneously:

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

$\displaystyle y = -2x + x + 9$

Can you do this?

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 ??