Question

For the function f(x)=-2(x-4)²+2, what is the axis of symmetry, and how can it be determined?

A) Axis of symmetry :x=4, determined by finding the vertex of the quadratic function.
B) Axis of symmetry:x=-4, determined by solving the equation x-4=0
C) Axis of symmetry: x=2, determined by taking the square root of the coefficient of x.
D) Axis of symmetry: x=0, determined by setting f(x)equal to zero.

Answer 1

The axis of symmetry for the function f(x)=-2(x-4)²+2 is x=4, determined by finding the vertex of the quadratic function.

Step-by-step explanation:

The axis of symmetry for the function f(x)=-2(x-4)²+2 is x=4. This can be determined by finding the vertex of the quadratic function.

The vertex form of a quadratic function is given by f(x)=a(x-h)²+k, where (h, k) represents the coordinates of the vertex. In this case, the vertex is (4, 2), so the axis of symmetry is the vertical line x=4.