I received a problem in my math class the other day that left me stumped. The problem went something like this.
Mr. Lots-O-Cash would like to order a parabola that passes through the points $(-4, 0)$, and $(2, 0)$. Create an equation for this so you can pass the information onto the manufacturing department.
I'm wondering, how can I find the equation for this parabola. It seems like to little info to find one. Please don't give me an answer, just a way to solve it.
Best Answer
The general form of a parabola/quadratic is:
$$y=ax^2+bx+c$$
You should be able to construct a pair of simultaneous equations using the two points and solve for $a,b,c$.
Another method is to consider:
$$y=\lambda(x-\alpha)(x-\beta)$$
Where $\alpha , \beta$ are the roots of the parabola.