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