+78 completing the square of the polynomial P(x) = x^2-6x+10 gives that P(x) = (x-3)^2+1. Decide which of the following statements about P(x) is correct.
1. the polynomial P(x) has at least one zero.
2. the minimum value of the polymonial P(x) is 1
3. the polynomial P(x) has a minimun of x=3
4.the polynomial P(x) is the zero x= -3
+23252 By writing the function as P(x) = (x - 3)2 + 1, you are showing that the minimum y-value of the function is 1.
[Since (x - 3)2 has either a value of 0 or a positive value for any choice of x, the graph rises from the minimum value, which occurs when the value of (x - 3)2 = 0. When the "+1" is added, the minimum y-value must be 1.]
Since the minimum y-value must be 1, choice 1) is incorrect because zeroes occur only when the y-value is 0.
Choice 2) is correct.
Choice 3) is incorrect because the minimum is 1, not 3.
Choice 4) is incorrect because there are no zeroes.
