<span>BC = 13
AC = 10
BD = x
We want to find what x is. You know what we can do? We can use the PYTHAGOREAN THEOREM. The PT states:

But we need to know DC in order to use the PT. But in Geometry there’s this theorem (I forgot sorry!) that states that BD divides ABD and CBD. Thus DC = 5 (half).
Pythagorean Theorem:

169 - 25 = 144

= 12
BD = 12.
Hope this helps!</span>
She needs six bases because a cube has six sides
G(x)=4x^2-16
To shift to the right we have to subtract from the value of x, in this case by 5 units...
h(x)=4(x-5)^2-16
h(x)=4(x^2-10x+25)-16
h(x)=4x^2-40x+100-16
h(x)=4x^2-40x+84
Now to shift the function downwards by 2 units we must subtract the constant 2 from h(x)
h(x)=4x^2-40x+84-2
h(x)=4x^2-40x+82