SOLUTION: Y=x^2 + 6x + 9 Identify the minimum value

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Y=x^2 + 6x + 9 Identify the minimum value      Log On


   

Question 558969: Y=x^2 + 6x + 9
Identify the minimum value
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+x%5E2+%2B+6x+%2B+9+
I know that the curve has a minimum and not
a maximum because the coefficient of the +x%5E2+ term
is (+) and not (-)
The form of the equation is +ax%5E2+%2B+bx+%2B+c+
The x coordinate of the minimum is at
+x%5Bmin%5D+=+-b%2F%282a%29+
+x%5Bmin%5D+=+%28-6%29%2F%282%2A1%29+
+x%5Bmin%5D+=+-3+
Now plug this back into the equation to get +y%5Bmin%5D+
+y%5Bmin%5D+=+%28-3%29%5E2+%2B+6%2A%28-3%29+%2B+9+
+y%5Bmin%5D+=+9+-+18+%2B+9+
+y%5Bmin%5D+=+0+
The minimum is at (-3,0)
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+%2B+6x+%2B+9+%29+