Step-by-step explanation:
soln;
given; p(x) = x^4 - 3x^3 - 6x^2 + 9
using remainder theorem;
p(x) = p(a)
= p(2)
= (2)^4 - 3(2)^3 - 6(2)^2 + 9
= -23
With the information given, we deduce that the parabola is

Reflecting a function over the x axis means to change its sign. After the reflection, the parabola becomes

And to shift down a function, you subtract the shift from the equation: the equation becomes

Similarly, the other function is reflected over the x axis (sign change) and shifted up 3 (add 3 to the equation):

In order to compute the y intercept, we simply have to evaluate the functions at x=0: for the parabola we have

For the other function, we have

3^4 = 3 x 3 x 3 x 3
4^3 = 4 x 4 x 4
3^3 = 3 x 3 x 3 = 27
Hope it helps!