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how do i find the minimum

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1 Answer

Hi again L;
y = x2 - 4x - 32
As you already know, this is a parabola.  The x2 is positive.  Therefore, it is opening upward.  The minimum corresponds to the line-of-symmetry.
This is NOT...
y=-b/2a
This is...
x=-b/2a
x=[(-(-4)]/[(2)(1)]
x=4/2
x=2
y = x2 - 4x - 32
y=(2)2-(4)(2)-32
y=4-8-32
y=4-40
y=-36
The lowest point is (2,-36).
 
An alternate approach is to consider the fact that the minimum corresponds to the point at which the change of y is zero.  Therefore, we can take the first derivative of the equation and calculate this...
y = x2 - 4x - 32
0=2x-4
4=2x
2=x

Comments

The lowest point is not (0,36), it's (2,-36).