x²-5x+2m=-1
You asked:
Investigate the equation: \({x}^{2} - 5 x + 2 m = -1\).
MathBot Answer:
The graph of the equation \({x}^{2} - 5 x + 2 m = -1\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{21}{8}, \frac{5}{2}\right)\)
The coordinates of its focus are: \(\left(\frac{17}{8}, \frac{5}{2}\right)\)
The directrix has equation: \(- 2 m + \frac{25}{4} = 0\).
The parabola has parameterization: \[\begin{aligned}m\left(\theta\right) &= \frac{21}{8} - \frac{\theta^{2}}{2}\\x\left(\theta\right) &= \frac{5}{2} + \theta\end{aligned}\]