Question

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

Minimum; (2, -3)

Maximum; (2, -3)

Minimum; (-3, 2)

Maximum; (-3, 2)

Answer 1

because x^2 is +1x^2 it is concave up, therefore it has a min value

Answer 2

no wonder students get so damned confused
the minimum value of a function is a NUMBER not an ordered pair
they are asking for the vertex of the parabola

Answer 3

first coordinate of the vertex is always
\[-\frac{b}{2a}\] in your case it is \[-\frac{-4}{2\times 1}=2\]

Answer 4

so x=2 but then what is the other number?

Answer 5

whatever you get for \(y\) when you replace \(x\) by 2

Answer 6

perhaps the wording of the problem could be better
yes that min is called the vertex just like satellite73 stated earlier

Answer 7

don't forget if you know the first coordinate, you can find the second by substitution

Answer 8

so then 2,-3

Answer 9

yes and don't forget it is a min