Determine whether the graph of y = x2 − 4x + 1 has a maximum or minimum point, then find the maximum or minimum value.

I know the point is (2, -3)
The first term is positive, so it has a minimum, right?

Question

Determine whether the graph of y = x2 − 4x + 1 has a maximum or minimum point, then find the maximum or minimum value.

I know the point is (2, -3)
The first term is positive, so it has a minimum, right?

anonymous · Answer

That is not how it is determined to be a maximum or a minimum. If it is a maximum, then the graph was increasing before the point, and decreasing afterwards, and vice versa for minimums. Or if you're okay with finding the second derivative, you can check if the second derivative is positive or negative at that point. If it is negative, then the graph is curving downwards, meaning you have a maximum, and vice versa. Does that help?

amistre64 · Answer

first term positive, has the shape of a U,  so yes, the vertex is a minimum point on the parabola

anonymous · Answer

Wait, then what did he mean by first term?

amistre64 · Answer

in algebra/trig ... they dont base it on derivatives ....

amistre64 · Answer

$$y=ax^2 + bx+c$$

if a>0, the vertex is minimum
if a<0, the vertex is maximum

anonymous · Answer

What the freak is a derivative .-.

anonymous · Answer

Oh, I don't remember doing this in algebra/trig, sorry Sephi! >.<

amistre64 · Answer

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