The top 5 things I learned in Pre-Calc 11 are
Graphing Reciprocal Fractions
So our quadratic function is
We would graph out our quadratic
Then to figure out our reciprocal we would put the equation as a denominator for a fraction (Forgot how to make it a fraction)
After finding the (x,y) for the equation then you can plug it in.
and that is how you find the reciprocal for a Quadratic Function
Finding the Standard form from General form
to find the standard or vertex form we have to complete the square.
On the left side we put brackets in to separate the C to find the perfect square for the brackets to find the to find the standard form
On the right side we take out c and put it with y and just did the same thing like we did on the left side
Finding the discriminant
To find the discriminant we have to use
we plug in the numbers and when we find the answer that is our discriminant.
The discriminant tells us how many roots our equation has…
so if x>0 we have two roots
if x=0 we have one root
if x<0 we have no roots
so in this equation above, we have two roots
and rationalizing radicals
(For example… )
So for example…
So, you would need to multiply it by the radical.
which would turn into..
then that would become
and the final result is
Which would be simplified into
Now that is how to rationalize a fraction.