for g(x)=x^2+2x+2, what is the function' s minimum or maximum value?
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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) = 1x^2 + 2x + 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 :)
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