Identify the conic section $$$y = \left(x - 1\right) \left(2 x - 6\right)$$$

Identify and find the properties of the conic section $$$y = \left(x - 1\right) \left(2 x - 6\right)$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = 2$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = -8$$$, $$$E = -1$$$, $$$F = 6$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = -2$$$.

Next, $$$B^{2} - 4 A C = 0$$$.

Since $$$B^{2} - 4 A C = 0$$$, the equation represents a parabola.

To find its properties, use the parabola calculator.

$$$y = \left(x - 1\right) \left(2 x - 6\right)$$$A represents a parabola.

General form: $$$2 x^{2} - 8 x - y + 6 = 0$$$A.

Graph: see the graphing calculator.