Note especially the technique for determining a quadratic function given some information about its values. Look back at problems involving exponential functions, linear functions, and variation. Observe that there is a common thread running through all these, namely, plug numbers in a general formula and solve equations to find the constants that appear in the function formula. You may then surmise that a similar approach will work when you encounter other functions later in life. You will be corredt in your surmise.
Some folks feel more confident if they have a formula to use.
This is a formula for the second coordinate of the vertex and so also gives the extreme value for the function. But, different strokes for different folks, as they say. If you like this formula, go ahead and use it. It's no skin off my teeth.