Answer:
a = -0.3575
Step-by-step explanation:
The points A and D lie on the x-axis, this means that they are the x-intercepts of the parabola, and therefore we can find their location.
The points A and B are located where
[tex]y=a(x+1)(x-5)=0[/tex]
This gives
[tex]x=-1[/tex]
[tex]y=5[/tex]
Now given the coordinates of A, we are in position to find the coordinates of the point B. Point B must have y coordinate of y=2 (because the base of the trapezoid is at y=0), and the x coordinate of B, looking at the figure, must be x coordinate of A plus horizontal distance between A and B, i.e
[tex]B_x=A_x+\frac{2}{tan(60)} =-1+\frac{2\sqrt{3} }{3}[/tex]
Thus the coordinates of B are:
[tex]B=(-1+\frac{2\sqrt{3} }{3},2)[/tex]
Now this point B lies on the parabola, and therefore it must satisfy the equation [tex]y=a(x+1)(x-5).[/tex]
Thus
[tex]2=a((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)[/tex]
Therefore
[tex]a=\frac{2}{((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)}[/tex]
[tex]\boxed{a=-0.3575}[/tex]
