Question

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?

a) 4
b) 10
c) 21
d) 25

Answer 1

To begin writing the function in vertex form, we need to add one zero pair to the given quadratic equation.

Step-by-step explanation:

To write the function in vertex form, we need to complete the square by adding zero pairs to the quadratic equation. The general form of a quadratic equation is f(x) = ax² + bx + c. In this case, the equation is f(x) = x² – 10x – 4. To begin writing it in vertex form, we can rearrange it as f(x) = (x² – 10x) – 4. Now, we can complete the square by adding the square of half the coefficient of x to both sides of the equation. Half of -10 is -5, so we add (-5)² = 25 to both sides. The equation becomes f(x) = (x² – 10x + 25) – 4 - 25. Simplifying further, we get f(x) = (x - 5)² - 29.

To write the equation in vertex form, we needed to add one zero pair, which is the square of half the coefficient of x. Therefore, the correct option is a) 1.