SOLUTION: I would appreciate your help on this: f(x)=-2x^2+2x+6. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. This

Algebra ->  Graphs -> SOLUTION: I would appreciate your help on this: f(x)=-2x^2+2x+6. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. This      Log On


   

Question 636699: I would appreciate your help on this: f(x)=-2x^2+2x+6. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.
This is what I have so far.
x coordinate of the vertex is 1/2
the y-coordinate of the vertex is_____
the equation of the line of symmetry is x=
The maximum /minimum of f(x)is_____
The value f(1/2)=13/2 is maximum
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+-2x%5E2+%2B+2x+%2B+6+
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+-2+
+b+=+2+
+c+=+6+
---------
+-b+%2F+%282a%29+=+-2%2F%282%2A%28-2%29%29+
+-b+%2F+%282a%29+=+1%2F2+
+x%5Bmax%5D+=+1%2F2+
Now plug this back into equation
+f%281%2F2%29+=+-2%2A%281%2F2%29%5E2+%2B+2%2A%281%2F2%29+%2B+6+
+f%281%2F2%29+=+-1%2F2+%2B+1+%2B+6+
+f%281%2F2%29+=+13%2F2+
This is y-co-ordinate of vertex
There is a maximum at ( 1/2. 13/2 )
+x+=+1%2F2+ is equation of line of symmetry
+y%5Bmax%5D+=+13%2F2+
----------------
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+10%2C+-2x%5E2+%2B+2x+%2B+6+%29+