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?

O 4
O 10
O 21
O 25

Answer 1

Zero pairs must be added to the function f(x) = x2 - 10x - 4 is O 4

Step-by-step explanation:

To write the quadratic function
`\(f(x) = x^2 - 10x - 4\)` in vertex form
`(\(f(x) = a(x - h)^2 + k\))`, you need to complete the square. The number of zero pairs to be added is determined by the coefficient of the
`\(x^2\)` term, which is 1 in this case. You need to add
`\((1)/(2) * (\text{coefficient of } x)^2\)` zero pairs.

So,
`\( (1)/(2) * (10)^2 = (1)/(2) * 100 = 50 \)`. However, since each zero pair contributes two zeros, you need
`\( (50)/(2) = 25 \)` zero pairs.

Therefore, the correct answer is O 25.