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
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