Question 356772
find the vertex of the x and y coordinate, line of symmetry and maximum of f(x)
f(x)=-2x^2+2x+7



f(x) = -2x^2 + 2x + 7, this is of form f(x) = ax^2 + bx + c
a = -2, a < 0, so parabola opens downwards


f(x) = -2x^2 + 2x + 7 is standard form of the parabolic equation
converting to vertex form
f(x) = -2(x^2 - x) + 7
(-1/2)^2 = 1/4
-2 * 1/4 = -2/4 = -1/2
7 + 1/2 = 7 1/2 = 15/2
the above 3 lines were completing the square to get below line
f(x) = -2x^2 + 2x - 1/2 + 7 + 1/2 = -2(x^2 - x + 1/4) + 15/2
f(x) = -2(x - 1/2)^2 + 15/2


this is now in vertex form of f(x) = a(x - h)^2 + k, where (h,k) is vertex


vertex is (1/2,15/2)


axis of symmetry -> x = h = 1/2


maximum of f(x) since parabola opens downwards is k or 15/2