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.
4 answers
Oh, the function should be f(x)=2x^2+100 right?
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
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
I'm a little confused: Why isn't x+10 squared?
Oh never mind, I got it! Thank you so much. This helps a lot!! :)
1 answer