how many more unit tiles must be added to the function f(x)=x² - 6x + 1 in order to complete the…
how many more unit tiles must be added to the function f(x)=x² - 6x + 1 in order to complete the square?\n1\n6\n8\n9
Answer
Explanation:
Step1: Recall the perfect - square formula
The perfect - square formula for a quadratic function of the form (y = ax^{2}+bx + c) is ((x + m)^{2}=x^{2}+2mx + m^{2}). For the given function (f(x)=x^{2}-6x + 1), where (a = 1), (b=-6), and (c = 1).
Step2: Determine the value to complete the square
In the formula (x^{2}+bx + c), to complete the square, we take half of the coefficient of (x), square it. The coefficient of (x) is (b=-6). Half of it is (\frac{b}{2}=\frac{-6}{2}=-3), and its square is ((\frac{b}{2})^{2}=(-3)^{2}=9). We currently have (c = 1), so the number of additional unit tiles needed is (9 - 1=8).
Answer:
8