plotting a quadratic

James Tanton has several interesting quadratic graph plotting techniques
based on the vertical line of symmetry
he introduces these amongst his various you tube offerings

when sketching a quadratic, instead of completing the square he suggests factorising the non-constant terms - to easily locate two values with the same y-ordinate:

x = 0 or 5 both give y-values = 3

so the curve must be symmetrical about a vertical line mid-way between these two  x values
(at x = 2.5), enabling the lowest point (vertex) of the quadratic to be calculated

this lowest point (vertex) can also be located by considering the lowest point of  y = x(x - 5) and then translating this 3 spaces up