Any help with the following questions is appreciated

Linear/Non-Linear Systems of Equations

1. Write an equation to form a system with so that the system has (2,9) as its only solution.

Answer is

But how do i get that answer?

2. The range of the graph is: ?

Quadratic Functions

1. What is the new equation when is translated 5 units left and 3 units down?

Quadratic Equations

1. Determine the values of K so that the graph crosses the x-axis twice.

Im wondering how to tell if i need a greater/less or equal sign (I think it is > for 2 real roots, < 2 unreal, = roots that are equal) also why it switched on the last step from -4k>-16 to K<4

Polynomial Functions/Equations

1. What are the zeroes of ?

I got

But i think there are others?