The top 5 things I learned in Pre-Calc 11 are

Graphing Reciprocal Fractions

So our quadratic function is $y=x^2+2$

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 $b^2 -4(a)(c)$

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

Factoring trinomials

(For example… $\frac 1 {5\sqrt{3}}$ $\cdot$$\frac {5\sqrt{3}} {5\sqrt{3}}$)

So for example… $\frac 1 {3\sqrt{3}}$

So, you would need to multiply it by the radical. $\frac 1 {3\sqrt{3}}$ $\cdot$ $\frac {3\sqrt{3}} {3\sqrt{3}}$

which would turn into.. $\frac {3\sqrt{3}} {9\sqrt{9}}$

then that would become $\frac {3\sqrt{3}} {9 \cdot 3}$

and the final result is $\frac {3\sqrt{3}} {27}$

Which would be simplified into $\frac {\sqrt{3}} {9}$

Now that is how to rationalize a fraction.

Week 18 – Top 5 things I learned in Pre-Calc 11