Question

Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-intercept, and vertex of the function.

f(x) = -2(x − 1)(x + 3)

Answer 1

The axis of symmetry is x = 1. The x-intercepts are 1 and -3. The y-intercept is 6.

Step-by-step explanation:

To find the axis of symmetry, we need to determine the x-coordinate of the vertex. The vertex of a quadratic function in the form f(x) = a(x - h)^2 + k is given by (h, k). In this case, the function is in the form f(x) = -2(x - 1)(x + 3), so the vertex is (1, 0).

The axis of symmetry is a vertical line that passes through the vertex. In this case, the axis of symmetry is the line x = 1.

To find the x-intercepts, we set f(x) = 0 and solve for x. In this case, f(x) = -2(x - 1)(x + 3), so we have:
-2(x - 1)(x + 3) = 0
Solving this equation, we find that the x-intercepts are x = 1 and x = -3.

To find the y-intercept, we substitute x = 0 into the function. In this case, f(x) = -2(x - 1)(x + 3), so the y-intercept is f(0) = -2(0 - 1)(0 + 3) = 6.