Hello, TH1!
You're a US general serving in Iraq and have been given orders to bomb a target 20km away.
The missile launcher has been programed with an equation
showing the parabolic trajectory of the missile.
If the equation is given in the general form $\displaystyle y \:=\:ax^2+bx+c$,
how can you know if it will hit the target?
Code:

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(0,0) (20,0)
We know two points on the parabola: .$\displaystyle (0,0)$ and $\displaystyle (20,0)$.
Plug them into the general equation: .$\displaystyle y \;=\;ax^2 + bx + c$
$\displaystyle (0,0)\!:\;\;0 \;=\;a\!\cdot\!0^2 + b\!\cdot\!0 + c\quad\Rightarrow\quad c \,=\,0$
. . The equation (so far) is: .$\displaystyle y \;=\;ax^2 + bx$
$\displaystyle (20,0)\!:\;\;0 \;=\;a\!\cdot\!20^2 + b\!\cdot\!20\quad\Rightarrow\quad b \:=\:20a$
. . The equation is: .$\displaystyle \boxed{y \;=\;ax^2  20ax}$
Note: Since we want a downopening parabola, $\displaystyle a < 0$.
If the general doesn't care how high the missile goes,
. . $\displaystyle a$ can be any negative quantity.