Math Problem Solver

The graph of the equation $y = 4 x - 7 {x}^{2}$ is a parabola.

The coordinates of its vertex are: $\left(\frac{2}{7}, \frac{4}{7}\right)$

The coordinates of its focus are: $\left(\frac{2}{7}, \frac{15}{28}\right)$

The directrix has equation: $- 28 y + 17 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= \frac{2}{7} + \theta\\y\left(\theta\right) &= \frac{4}{7} - 7 \theta^{2}\end{aligned}$$