How do you find the max and min of y=-x^2+6 by completing the square?

1 Answer
Alan P.
May 9, 2015

"Completing the squares" is a bit unusual for the given equation:
y=-x^2+6
since in "completed square form" it would be:
y = (-1)(x^2-0x+0)+6
or
y=(-1)(x-0)^2+6

This is also the vertex form;
so the vertex is at (0,6)

Because of the (-1) factor we know that the parabola opens downward rarr the vertex is at a maximum.
As the magnitude of x increases the value of y decreases without bound.

So the maximum value is 6 and the minimum is -oo

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