1. The problem statement, all variables and given/known data
10) Two numbers have a sum of 13.
10)a) Find the minimum of the sum of their squares.
10)b) What are the two numbers
2. Relevant equations
y = ax^2 + bx + c
y = a (x-h)^2 + k
According to the text: for a quadratic function in the forum of y=a(x-h)2+k, the maximum or minimum value is k, when x=h. If a> 0, k is the minimum value of the function. If a <0, k is the maximum value of the function.
3. The attempt at a solution
No attempt, do not understand how to properly attempt the question.
What I believe to understand is that
a) the question is asking for the value of two numbers which add up to 13, and
b) what the value of those two numbers squared, then added up together is. I don't understand why it's asking for the "minimum" value of their squares.
It's simple enough to just divide 13 by 2 and then square those two numbers, logically you would arrive with the sum being the smallest of all possible numbers.
The problem is working out the correct way to do it, involving the quadratic formula.
I'm taking this math course at night school, which means the program is accelerated and the teacher is less willing to help, for both person reasons (bad teacher), and the fact that they are probably tired from teaching all day already.
So I am exercising the option to ask the internet (math help forum).