Here are the solutions to the problems:

1. 8(a): $4x^2 + 2x + 5 = 4(x + 0.25)^2 + 4.9375$

2. 8(b): The function $4x^2 + 2x + 5$ does not meet the x-axis.

3. 9(a): The expression $8x^3 - 2x^2 - 8x - 1$ is already simplified and cannot be factored further into simpler linear and quadratic terms.

4. 9(b): The stationary points of the function are at $x = -\frac{1}{2}, \frac{2}{3}$. At $x = -\frac{1}{2}$, the function value is $\frac{3}{2}$.

5. 10(a): The smallest value of $g(x) = x^3 - 5x$ is $-\frac{10\sqrt{15}}{9}$.

6. 10(b): The function $f(x)$ such that $f'(x) = \frac{1}{x^3 - 5x}$ is $f(x) = -\frac{\log(x)}{5} + \frac{\log(x^2 - 5)}{10}$.

7. 11(a): The expression $2x^2 - 7x$ in the form $p[(x - q)^2 - r]$ is $6.125(0.5714x - 1)^2 - 4.125$.

8. 11(b): The range of the function $g(x) = 2x^2 - 7x$ is $[18.375, \infty)$.

Do you have any questions or need further details? Here are some related questions:

1. How to complete the square for other quadratic functions?
2. What does the discriminant tell us about the roots of a quadratic equation?
3. How to find and classify stationary points for different functions?
4. What are the implications of a function's derivative on its behavior?
5. How can you determine the range of a quadratic function?

Tip: When solving for the stationary points of a cubic function, always evaluate the first derivative and solve for where it equals zero.