Argumentative essay on College Algebra. Needs to be 2 pages. unction with repeated factors (even multiplicity) is: x2 +6x + 9 with repeated factors (x + 3)2, therefore, it touches the x-axis only at point x= -3 and does not cross the x-axis as shown in the graph below.The turning point of a graph is the point that a graph changes direction form decreasing to increasing or from increasing to decreasing. Turning points can also show the maximum point, minimum point and point of inflection.To determine the number of turning point, the degree of polynomial is lessened by one (n – 1) where n is the degree of polynomial. therefore the turning point of its graph is always less than the degree of the polynomial. For example, a polynomial of degree 4 will have 3 turning points or even less as can be seen in the two graphs