A= 1/2 * (21 - h) * h
You asked:
Investigate the equation: \(A = \frac{1}{2} \cdot \left(21 - h\right) \cdot h\).
MathBot Answer:
The graph of the equation \(A = \frac{1}{2} \cdot \left(21 - h\right) \cdot h\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{441}{8}, \frac{21}{2}\right)\)
The coordinates of its focus are: \(\left(\frac{437}{8}, \frac{21}{2}\right)\)
The directrix has equation: \(- 2 A + \frac{445}{4} = 0\).
The parabola has parameterization: \[\begin{aligned}A\left(\theta\right) &= \frac{441}{8} - \frac{\theta^{2}}{2}\\h\left(\theta\right) &= \frac{21}{2} + \theta\end{aligned}\]