1. Determine the graph behavior at the zero(s) of the polynomial function f(x)=x^2 - 6x + 9.
A. The graph of the function touches the x-axis at x = -3 and x = 3.
B. The graph of the function crosses the x-axis at x = -3 and x = 3.
C. The graph of the function touches the x-axis at x = 3.
D. The graph of the function crosses the x-axis at x = -3.
The answer is: [C]: ________________________________________________ "The graph of the function touches the x-axis at x = 3." ________________________________________________ Explanation: ________________________________________________ Write the function as the following equation: ________________________________________________ x² − 6x + 9 = 0 . _______________________________________ Factor the "left hand side of the equation": _______________________________________ (x −3) (x − 3) = 0 . ________________________________________ → Solution: x = 3 (when y = 0). _______________________________________ The answer is: [C]: ________________________________________ "The graph of the function touches the x-axis at x = 3." _____________________________________________________
