SOLUTION: f(x)=1/2x^2+6x+11 Use the vertex formula to find the vertex. Type answer as an ordered pair. Simplify.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: f(x)=1/2x^2+6x+11 Use the vertex formula to find the vertex. Type answer as an ordered pair. Simplify.      Log On


   

Question 486883: f(x)=1/2x^2+6x+11
Use the vertex formula to find the vertex.
Type answer as an ordered pair. Simplify.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation is in the form
+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+, the vertex
is at +x+=+-b%2F%282a%29+
+f%28x%29=+%281%2F2%29%2Ax%5E2+%2B+6x+%2B+11
+-b%2F%282a%29+=+-6%2F%282%2A%281%2F2%29%29+
+-b%2F%282a%29+=+-6+
Now put this value of +x+ into the
equation to find +y+, or +f%28x%29+.
+f%28x%29=+%281%2F2%29%2A%28-6%29%5E2+%2B+6%2A%28-6%29+%2B+11
+f%28x%29+=+18+-+36+%2B+11+
+f%28x%29+=+-7+
The vertex is at (-6, -7)
Here is a plot:
+graph%28+400%2C+400%2C+-14%2C+6%2C+-10%2C+10%2C+%281%2F2%29%2Ax%5E2+%2B+6x+%2B+11%29+