Using the completing-the-square method, rewrite f(x) = x² + 10x + 7 in vertex form.

Solution:

The vertex form of the equation is given by

f(x) = a(x - h)²+ k

Given, f(x) = x² + 10x + 7

Converting to vertex form,

x² + 10x + 7 = x² + 10x + 7 + 25 - 25

It can be written as

f(x) + 25 = (x + 5)² + 7

So we get

f(x) =  (x+ 5)² + 7 - 25

f(x) =  (x + 5)² - 18

Therefore, the equation in vertex form is  f(x) = (x + 5)² - 18.

Using the completing-the-square method, rewrite f(x) = x² + 10x + 7 in vertex form.

Summary:

Using  the completing the square method, the equation f(x) = x² + 10x + 7 in vertex form is f(x) = (x + 5)² - 18.