Question

Determine the axis of symmetry for the function f(x) = −2(x + 3)² − 5.

a. x = 3
b. x = −3
c. x = 5
d. x = −5

Answer 1

The axis of symmetry for the function f(x) = −2(x + 3)² − 5 is determined by the vertex of the parabola, which is given by setting the expression within the brackets to zero. The axis of symmetry is therefore x = -3, matching option b. x = −3.

Step-by-step explanation:

To determine the axis of symmetry for the function f(x) = −2(x + 3)² − 5, we need to look at the general form of the quadratic equation, which is f(x) = a(x - h)² + k. Here, h represents the x-coordinate of the vertex of the parabola, and thus the line x = h is the axis of symmetry.

In the given function, the equation is in the form f(x) = a(x + 3)² + k, with a slight modification of the sign inside the brackets. The x-coordinate of the vertex can be found by setting the expression within the brackets to zero: x + 3 = 0. Solving for x gives us x = -3.

Therefore, the axis of symmetry for the function is x = -3. The correct answer is b. x = −3.