I must ask you what in the world that posting means?
It seems to be just series of meaningless statements.
What are you on about?
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.
But how do i get that answer?
2. The range of the graph is: ?
1. What is the new equation when is translated 5 units left and 3 units down?
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
1. What are the zeroes of ?
But i think there are others?
So let's assume we have a new equation of the form .
So solve the system
such that the solution is (2, 9).
I'll start you off:
Put the solution point into the second equation:
Thus the second equation is
Now we need to solve the system
See what you can do with this.
When we translate this graph h units to the right the corresponding function is .
When we translate this graph h units to the left the corresponding function is .
When we translate this graph k units up the corresponding function is .
When we translate this graph k units down the corresponding function is .
See if you can apply these rules to get your answer.
Whenever you divide both sides of an inequality by a negative number the inequality changes "direction." So
If you have troubles seeing this, consider a simpler example. Solve
You can easily get the solution set from the given inequality, and you should be able to see that it is , which is what you get when you divide both sides by -1.
Why should there be other zeros?
The concept behind solving something like this is the following theorem:
If ab = 0 then either a = 0 or b = 0 or both.
So when we a simpler example like
(and we can't have both terms equal to 0 at the same time.) You've likely seen this process any number of times when solving a quadratic that factors.
In this case we have:
<-- Not true!
So we have
or more simply