(X-5)²+7=2x
You asked:
Investigate the equation: \({\left( X - 5 \right)}^{2} + 7 = 2 x\).
MathBot Answer:
The graph of the equation \({\left( X - 5 \right)}^{2} + 7 = 2 x\) is a parabola.
The coordinates of its vertex are: \(\left(5, \frac{7}{2}\right)\)
The coordinates of its focus are: \(\left(5, 4\right)\)
The directrix has equation: \(2 x - 6 = 0\).
The parabola has parameterization: \[\begin{aligned}X\left(\theta\right) &= 5 + \theta\\x\left(\theta\right) &= \frac{7}{2} + \frac{\theta^{2}}{2}\end{aligned}\]