Short Answer 
The first step involves understanding the parabola equation, identifying its roots at x = -1 and x = 5, which define key points for the trapezoid. Next, the properties of an isosceles trapezoid with a height of 2 units and 60-degree angles at vertices A and D provide necessary geometric relationships. Finally, by substituting known values into the parabola equation based on the trapezoid’s vertices, we can solve for the coefficient ‘a’.
Step 1: Understand the Parabola Equation
First, we need to recognize the structure of the parabola given by the equation y = a(x + 1)(x – 5). This format indicates that the roots of the parabola are located at x = -1 and x = 5. These roots help us establish crucial points on the parabola where vertices of the trapezoid will be located. Additionally, determining the vertex and the direction of the parabola is critical to understanding its geometry.
Step 2: Analyze the Isosceles Trapezoid Properties
Next, develop a geometric understanding using the properties of the isosceles trapezoid that has a height of 2 units and angle measures of 60 degrees at vertices A and D. The trapezoid’s dimensions‚Äîalong with the positions of its bases‚Äîallow us to approximate the y-coordinates of points A and D, which will help us derive equations to solve for a. With this shape, we can leverage both the trapezoid’s dimensions and its angles to set up relationships between the points and the parabola.
Step 3: Solve for Coefficient ‘a’
In the final step, we will solve for the coefficient a by substituting known values into the parabola equation derived from the trapezoid’s vertices. Set the height corresponding to the y-coordinates for points A and D (both on the x-axis) into the parabola’s equation. Utilizing the properties of the trapezoid and the fact that these points satisfy the parabola’s equation will help us create a system of equations to isolate and calculate the value of a, achieving our objective.