Answer:
[tex]a=-0.35747[/tex]
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 [tex]y=0[/tex]
Therefore points A and D are located where
[tex]a(x+1)(x-5)=0[/tex]
[tex]A=x=-1[/tex]
[tex]D=x=5[/tex]
Now we need to find the coordinates of point C; we already have its y-coordinate (it's [tex]y=2[/tex]), and looking at the figure attached we see that the x-coordinate of point C is [tex]\frac{2}{tan(60^o)}[/tex] farthar from the coordinate of point C; thus
[tex]C_x=\frac{2}{tan(60^o)}-1=0.1547[/tex]
Therefore the coordinates of C are [tex]C=(0.1547,2)[/tex]
Now this point C lies on the parabola, and therefore must satisfy the equation [tex]y=a(x+1)(x-5):[/tex]
[tex]2=a(0.1547+1)(0.5147-5)[/tex]
[tex]\therefore a=\frac{2}{(0.1547+1)(0.5147-5)} =-0.35747\\\\\boxed{a=-0.35747}[/tex]
