49x^2 +42x + c=0
You asked:
Investigate the equation: \(49 {x}^{2} + 42 x + c = 0\).
MathBot Answer:
The graph of the equation \(49 {x}^{2} + 42 x + c = 0\) is a parabola.
The coordinates of its vertex are: \(\left(9, - \frac{3}{7}\right)\)
The coordinates of its focus are: \(\left(\frac{1763}{196}, - \frac{3}{7}\right)\)
The directrix has equation: \(- 196 c + 1765 = 0\).
The parabola has parameterization: \[\begin{aligned}c\left(\theta\right) &= 9 - 49 \theta^{2}\\x\left(\theta\right) &= - \frac{3}{7} + \theta\end{aligned}\]