Graph of $$$y = f{\left(x \right)} = - \left(x + 8\right)^{2} - 1$$$
To draw a parabola, circle, ellipse or hyperbola, choose the "Implicit" option.
You can pass a function as a parameter: https://www.emathhelp.net/calculators/calculus-1/online-graphing-calculator/?y=sin(x)&y=cos(x) will draw y=sin(x) and y=cos(x).
Related calculator: 3D Graphing Calculator
Pan the graph (move it) by holding the Shift key and dragging the graph with the mouse.
Zoom the graph in and out by holding the Shift key and using the mouse wheel.
The above operations can be very slow for more than 2 graphs. To avoid it, delete all graphs, pan and zoom, and then plot the graphs again.