Question

How many zero pairs must be added to the functionf(x) = x2 – 10x – 4 in order to begin writing the function in vertex form?

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

Answer 1

Option d. 25

Explanation:

Vertex form a quadratic equation is written in the form of f(x) = (x - h)² + k

where (h, k) is said to be the vertex of the equation.

Now we will try to convert the given quadratic function in the vertex form by adding zero pairs in the equation.

f(x) = x² - 10x - 4

= x² - 10x - 4 + (25 - 25) [Since (x² - 2.(5x) + 25) = (x - 5)² so we have added a zero pair 25]

= (x - 5)² - 4 - 25

= (x - 5)² - 29

= (x - 5)² + (-29)

Therefore, 25 is the zero pair that must be added to the given function to convert it in the vertex form

Option d. 25 is the answer.