Hi again L;
y = x^{2}  4x  32
As you already know, this is a parabola. The x^{2} is positive. Therefore, it is opening upward. The minimum corresponds to the lineofsymmetry.
This is NOT...
y=b/2a
This is...
x=b/2a
x=[((4)]/[(2)(1)]
x=4/2
x=2
y = x^{2}  4x  32
y=(2)^{2}(4)(2)32
y=4832
y=440
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 = x^{2}  4x  32
0=2x4
4=2x
2=x
1/12/2014

Vivian L.
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