Question

Let f(x)=ax^2-4x-c. A horizontal line, L, intersects the graph of f at x= -1 and x=3. The equation of the axis of symmetry is x = p. Find p?

a) p=−2
b) p=1
c) p=2
d) p=3

Answer 1

The axis of symmetry for the quadratic function provided is p = 1, which is option b). It lies exactly midway between the two points where the horizontal line intersects the graph.

Step-by-step explanation:

The student's question concerns a quadratic function and its properties, specifically the axis of symmetry and the points at which a horizontal line intersects the graph of the function. For a quadratic function f(x) = ax^2 - bx - c, the axis of symmetry is at x = -b/2a. Given that the horizontal line L intersects the graph of f at x = -1 and x = 3, the axis of symmetry must be midway between these two points, which means p = (3 + (-1))/2 = 1. Therefore, the correct answer is b) p = 1.