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In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:
y = x2
4 = x2
x = 2, -2
y = (0)2
y = 0
Which is, indeed, the vertex of y = x2
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