SOLUTION: Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and the graph function. {{{ f(x)= -2x^2+2x+2 }}} 1) The x-coordinate of th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and the graph function. {{{ f(x)= -2x^2+2x+2 }}} 1) The x-coordinate of th      Log On


   

Question 358581: Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and the graph function.

+f%28x%29=+-2x%5E2%2B2x%2B2+

1) The x-coordinate of the vertex is?? "simplified fraction"
2) The y-coordinate of the vertex is?? "simplified fraction"
3) The equation of the line of symmetry is x= ??? "simplified fraction"
4) The maximum/minimum of f(x) is ?? "simplified fraction"
5) The value f(1/2)=5/2 is maximum or minimum???
I am lost could someone please help me and show a graph as well please
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

The vertex form of a parabola is y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex



f%28x%29+=+-2x%5E2+%2B+2x+%2B+2

Completing the Square and putting it into the vetex form of a parabola

f%28x%29+=+-2%28x%5E2+-x+-+1%29

f%28x%29=+-2%28x%5E2+-x+%2B+1%2F4+-1%2F4+-1%29

f%28x%29=+-2%28x+-+1%2F2%29%5E2+-2%28+-1%2F4+-1%29

f%28x%29=+-2%28x+-+1%2F2%29%5E2+-2%28-5%2F4%29

f%28x%29=+-2%28x+-+1%2F2%29%5E2+%2B+5%2F2

a = -2   a < 0 parabola opens downward

The x-coordinate of the vertex 1s 1/2

The y-coordinate of the vertex is  5/2

The equation of the line of symmetry is x = 1/2

The maximum f(x) is 5/2

The value f(1/2)=5/2 is maximum