How do you find the maximum and minimum value of a quadratic function with no use of calculus?

By completing the square, since this makes you see that the square will always be >= 0 and the other part allows you to calculate the minima or maxima depending on the sign in front of x². E.g. x²+4x= (x+2)²-4, since the squre's min value is 0, the minimum value the function can take is -4. This will also help with A-level, since sometimes you can save time by using completing the square method insted of differentiation.