I have the first point is (0, -100) and the second point is (7500, -250), and the maximum point is at (x, 210).
Is it possible to find X or the equation of the parabola using this information alone?
If so how?
[Math] parabola equation given only two points
conic sections
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Best Answer
Assume you have $y=ax^2 + bx + c$. The maximum is achieved at $x = -\frac{b}{2a}$.
The values you have give you the value of $c$ ($-100$), and a relation between $a$ and $b$ obtained by plugging in $(7500,-250)$. You also know that the maximum is achieved at $-\frac{b}{2a}$, so plugging that will give you another relation between $a$ and $b$. Putting them together will give you a quadratic equation that $b$ must satisfied.