SOLUTION: Using {{{f(x)=-2x^2+2x+8}}}, find the x-coordinate of the vertex and the equation of the line of symmetry.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Using {{{f(x)=-2x^2+2x+8}}}, find the x-coordinate of the vertex and the equation of the line of symmetry.      Log On


   

Question 130757: Using f%28x%29=-2x%5E2%2B2x%2B8, find the x-coordinate of the vertex and the equation of the line of symmetry.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-coordinate of the vertex, we can use this formula:

x=-b%2F%282a%29

From the equation f%28x%29=-2x%5E2%2B2x%2B8 we can see that a=-2 and b=2

x=%28-2%29%2F%282%2A-2%29 Plug in b=2 and a=-2


x=%28-2%29%2F-4 Multiply 2 and -2 to get -4



x=1%2F2 Reduce


So the x-coordinate of the vertex is x=1%2F2


In turn, this means that the equation of the line of symmetry is also x=1%2F2 (since the line goes through the vertex)