Thread: Formula of Parabola = ??

1. Formula of Parabola = ??

How can you find in a simple way the formula of Parabola that passes
through the point $p(2,1)$ and passes through the points of intersection
of functions $y = x^2 + 3x + 7$ & $y = -2x^2 + x + 10$

2. Originally Posted by razemsoft21
How can you find in a simple way the formula of Parabola that passes
through the point $p(2,1)$ and passes through the points of intersection
of functions $y = x^2 + 3x + 7$ & $y = -2x + x + 9$
Step 1: Solve the following equations simultaneously:

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

$y = -2x + x + 9$

Can you do this?

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

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

$y = -2x + x + 9$

Can you do this?
sorry, the 2 equation are:

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

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

to get points of intersection:

$x^2 + 3x + 7$ = $-2x^2 + x + 10$
$3x^2 + 2x - 3 = 0$

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

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

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

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