### Question Description

for g(x)=x^2+2x+2, what is the function' s minimum or maximum value?

## Explanation & Answer

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

In order to find the minimum or maximum value of a quadratic function we just find the x coordinate of the vertex by using this expression:

x = -b/(2a) ; where a is the coeffcient of the x^2 (the number in front of the x^2)

b is the coefficient of the x (the number in front of the x).

So let's remember the x^2 can be written like 1x^2 (its coefficient is 1). So we would have:

g(x) = x^2 + 2x + 2 --------> g(x) = **1**x^2 + **2**x + 2 ---------> Here, we can see: a = 1 and b = 2.

Then we enter 1 in place of a and 2 in place of b into the expression like this:

x = - b/(2a) = - 2/(2*1) = -2/2 = -1 --------> **x = -1** (The minimum/maximum is reached at -1).

Finally, we find the minimum/maximum by entering -1 in place of x into the original function g(x) = x^2 + 2x + 2. So we have:

g(x) = x^2 + 2x + 2 -----------> g(-1) = (-1)^2 + 2(-1) + 2 ------------> g(-1) = 1 - 2 + 2 --------> **g(-1) = 1**

So the **minimum is 1** (it's a minimum since a is positive number, remember a = 1). So we can also write the ordered pair (x , y) which is **(-1 , 1)**.

Please let me know if you have any doubt or question :)