how many zero pairs must be added to the function f(x)=x² - 10x - 4 in order to begin writing the function…
how many zero pairs must be added to the function f(x)=x² - 10x - 4 in order to begin writing the function in vertex form?\n4\n10\n21\n25
Answer
Explanation:
Step1: Recall vertex - form formula
The vertex - form of a quadratic function is (y=a(x - h)^2+k), and for the quadratic function (y = x^{2}+bx + c), we complete the square. Given (f(x)=x^{2}-10x - 4), where (b=-10).
Step2: Use the completing - the - square rule
To complete the square for (x^{2}+bx), we add and subtract ((\frac{b}{2})^2). Here, (b=-10), so ((\frac{b}{2})^2=(\frac{-10}{2})^2 = 25). Adding and subtracting 25 is equivalent to adding 25 zero - pairs (since (25-25 = 0)).
Answer:
25