For Min Turning points:
Say you have the equation
y=x2+4x+1, that can be written as:
y=(x+2)2−3.
To find the minimum turning point, you need find the point where y is at its lowest value. So therefore, you want the point where
(x+2)2−3 is at its lowest value. You can't do anything about the "-3" bit, that's a constant, but what you can do is to make
(x+2)2 as low as possible. You do that by making x = -2, so that you get
(−2+2)2=02, if x is any less, or any more, then you'll get a positive number for that part of the equation. The key is to make the value inside the brackets be 0.
So now you know x is -2, what is y? Well, you just plug in the values so you get
y=(−2+2)2−3=−3, this is just the value outside the brackets. So the minimum turning point for
y=x2+4x+1 is
(−2,−3). See if you can do the same for the maximum turning point of
y=−x2+4x+1