Question

F(x)=x2 + 4x -6

f(x) can be written in the form (x + m)?+n.
Find the value of m and the value of n.​

Answer 1

m = 2 and n = -10

Explanation:

The given function is f(x) = x² + 4·x - 6

The form in which f(x) is to be written = (x + m)² + n, which is the standard form of a quadratic equation

We have;

f(x) = x² + 4·x - 6 = x² + 4·x + 4 - 6 - 4

f(x) = x² + 4·x + 4 - 6 - 4 = (x + 2)² - 10

f(x) = (x + 2)² - 10

By comparison with (x + m)² + n, we have;

m = 2, and n = -10