Area (S) is 2. How do I find the equation of this parabola? ;\ I guess first of all I should start at this: $\displaystyle \int_{0}^1 ?? dx=2$ but it does not seem to help me at all...
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If the function whose graph is this parabola is $\displaystyle f(x)=ax^2+bx+c$, you have three unknowns: a, b and c. You also have three equations: $\displaystyle \int_0^1f(x)\,dx=2$, f(0) = 0 and f(1) = 0.
In other words, we know that x = 0 and x = 1 are roots, so x and (x - 1) are factors. So your quadratic is of the form ax(x - 1)...
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