​what's the easiest way to find the max and min of a quadratic equation?

If it's in this form,   y = ax^2  + bx + c      and "a" is positive, it will only have a min  [and no max]

If "a" is  negative,  it will only have a max  [ and no min]

If you know Calculus, you can find these very quicly, but, if not, the max [or min]  can be found thusly :

[ x , y ]    =    [ -b / 2a  ,   c - b^2/ 4a  ]

BTW - the max [ or min]  is known as the "vertex"

Example  :

y = 3x^2 - 2x + 5

This will have a min given by :

[ x, y ]  = [  - (-2)/ [ 2(3)] ,  5  - (-2)^2/ [ 4 * 3]  = [ 2/6 ,  5 - 4/12]   =  [ 1/3,  5 - 1/3] =

[ 1/3 , 14/3]

See the graph here, and note that this is a "min" because "a" is positive  :

https://www.desmos.com/calculator/vpqh11gmw0