@mathmate
@mathmate
Finally, got here!
Start with quadratic equations, ok?
ok :)
Solve \(x^2 -6x +9=0\)
a=1 b=-6 c=9
ok.
\[\huge~x=\frac{ -(-6)\pm \sqrt{(-6)^2-4(1)(9)} }{ 2(1) } \]
Great, now can you simplify that, because it will be greatly simplified when you put the numbers in there.
\[\huge~x=\frac{ 6\pm \sqrt{0} }{ 2}\]
\[\huge~\frac{ 6 }{ 2 }=3~~~~~x=3\]
Yes, that is the same as {3,3}, or 3 (twice)
It's called a double root, andthe graph looks like this:|dw:1433211976391:dw| the vertex just touches the x-axis.
ok so far?
ye
If you factored, you would have got (x-3)^2=0, which is the same as saying (x-3)=0, or x=3 (twice), or x={3,3}
Was wondering you still have the online textbook?
Can you dig some questions out of there, which will be more like what you have learned.
T_T but there are answers ,_,
You don't have to look at them, in any case, we are looking at the work, can check the answers at the end.
There may be word problems, which take more time to make. Using ready-made problems can help us do more.
Have you done anything like this? "A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?"
:/
no O_O
Always the numerical equations, and nothing like word problems?
no ._.
ok, so we can skip that.
:)
Whenever you solve quadratics, there are three ways to do it. If the teacher does not specify, you can use any method you want. If he/she specifies completing the square, you have no choice. the three are:
quad formula (just did) factoring (did over the weekend) completing the square Do youknow how to do the last one?
no :/ we havent learned it
ok, so we skip that too. Anything else you'd like to do on quadratic equations/
Nope.
So we will move onto system of linear equations. Have you done word problems?
yes but dont like those :/
How many ways do you know to solve system of linear equations?
Elmination Substituion :/
comparison?
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