y = 3x - 5 + x^2
You asked:
Investigate the equation: \(y = 3 x - 5 + {x}^{2}\).
MathBot Answer:
The graph of the equation \(y = 3 x - 5 + {x}^{2}\) is a parabola.
The coordinates of its vertex are: \(\left(- \frac{3}{2}, - \frac{29}{4}\right)\)
The coordinates of its focus are: \(\left(- \frac{3}{2}, -7\right)\)
The directrix has equation: \(4 y + 30 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{3}{2} + \theta\\y\left(\theta\right) &= - \frac{29}{4} + \theta^{2}\end{aligned}\]