An isosceles trapezoid abcd with height 2 units has all its vertices on the parabola y=a(x+1)(x−5). what is the value of a, if points a and d belong to the x−axis and m∠bad=60o?

Step-by-step explanation:

We know that all the vertices of the isosceles trapezoid lie on the parabola, and the points A and D lie along the x-axis, i.e at

Therefore points A and D are located where

Now we need to find the coordinates of point C; we already have its y-coordinate (it's ), and looking at the figure attached we see that the x-coordinate of point C is farthar from the coordinate of point C; thus

Therefore the coordinates of C are

Now this point C lies on the parabola, and therefore must satisfy the equation