Express x^2+4x-7 in the form (x+a)^2-b where a and b are integers

Here, we are required to express x² + 4x - 7 in the form (x+a)² - b and determine the values of a and b.

By completing the square method;

a = (4/2) = 2.

Therefore, by expanding (x+a)² i.e (x+2)²

We therefore have; x² + 4x + 4

However, the question is given as x²+4x-7

Therefore, by comparison between;

x² + 4x + 4 and x²+4x-7; we have;

4 - b = -7, b = 7+4

Ultimately, b = 11

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(x + 2)^2 - 11.

Step-by-step explanation:

f(x) = x^2 + 4x - 7

Now x^2 + 4x = (x + 2)^2 - 4 so we have:

f(x) = (x + 2)^2 - 4 - 7

f(x) = (x + 2)^2 - 11.