Any help with the following questions is appreciated

Linear/Non-Linear Systems of Equations

1. Write an equation to form a system with $\displaystyle y=5x-1$ so that the system has (2,9) as its only solution.

Answer is $\displaystyle y=2x+5$

But how do i get that answer?

2. The range of the graph $\displaystyle y=\frac{1}{2}(x-12)^2+15$ is: ?

Quadratic Functions

1. What is the new equation when $\displaystyle y=(x-2)^2+9$ is translated 5 units left and 3 units down?

Quadratic Equations

1. Determine the values of K so that the graph $\displaystyle f(x)=x^2+4x+k$ crosses the x-axis twice.

$\displaystyle b^2-4ac>0$

$\displaystyle (4)^2-4(1)(k)>0$

$\displaystyle 16-4k>0$

$\displaystyle -4k>-16$

$\displaystyle k<4$

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 $\displaystyle 7(2x+3)^3(x-1) > 0$?

I got $\displaystyle x=\frac{-3}{2},1$

But i think there are others?