Question

One number is 10 larger than another. Write a function in standard form to represent the sum of their squares. The minimum sum of squares is ___.

So I said that the function is f(x)=x^2+x+10 and since the question comes from an assignment on completing the square to convert to vertex form, I completed the square and got f(x)=(x+1/2)^2-39/4. But, now I don<t know what to do to find the minimum sum.

Answer 1

Oh, the function should be f(x)=2x^2+100 right?

Answer 2

smaller number --- x
larger number ---- (x+10)

sum of their squares
= (x+10) + x^2
= x^2 + 20x + 100 + x^2
= 2x^2 + 20x + 100

this is a parabola opening upwards so it has a minimum.
That minimum happens at the vertex.
The x of the vertex is -20/4 = -5

so one number is -5, the other is +5
for a minimum of 25+25 = 50

Answer 3

I'm a little confused: Why isn't x+10 squared?

Answer 4

Oh never mind, I got it! Thank you so much. This helps a lot!! :)