Question

I have a question that has already been answered. I just need someone to please explain the steps.

Find the coordinates of the minimum point of the function- f(x) = x^2 + 4x - 5.

Solution-

We need to express x^2 + 4 - 5 in the form (x+h)^2 + k.

Let x^2 - 4x = (x - 2)^2 - 4 (Where did the -4 come from?)

x^2 + 4x - 5 = [ (x - 2)^2 - 4] - 5
= (x - 2)^2 - 9

All I wanna know is where the -4 came from. what rule must be applied. ​

Answer 1

Explanation:

Using brackets will really help.

y = (x^2 + 4x + ... ) - 5 You are trying to complete the square. The square in this case is a trinomial that is squared.

To do that, you take 1/2 the linear term (4x)/2, drop the x (4/2), and square the result (4/2)^2. The number is 2^2 which is 4.

So far what you have is

y = (x^2 + 4x + 4) - 5

Now you just can't add 4 without adjusting it somehow. If you do, the whole question will change it's value. Because you added 4 inside the brackets, you must subtract 4 outside the brackets.

What that means is 4 inside - 4 outside. So it looks like this

y = (x^2 + 4x + 4) - 5 - 4

Now you continue on

y = (x + 2)^2 - 9 The 4 combines with the 5 to make nine.