Find the coordinates of the vertex and the axis of symmetry

Find the coordinates of the vertex and the axis of symmetry of the graph of the equation. Use (-b/2a, f(-b/2a)) to find the vertex. (Simplify the coordinates of the vertex completely.) See Example 8. (Objective 7) f(x) =-2x^2 - 4x + 4 vertex (x, y) = () axis of symmetry Graph the equation.

Solution

For a quadratic function in standard form, f(x) = ax²+bx+c,

the axis of symmetry is x = b/2a.

Given that f(x) = -2x²+4x+4

            a = -2, b= 4, c=4

axis of symmetry:

      axis of symmetry is x = -b/2a= -4/2.-2 = 1

                                    x =1

Therefore,

axis of symmetry is x = 1

vertex:

Given that f(x) = -2x²+4x+4

vertex = (-b/2a, f(-b/2a))

f(-b/2a) = f (1) = -2.1² + 4.1 + 4 = 6

      -b/2a = 1

Therefore,

         vertex = (1,6)