## week 6 – precalc 11

This week we started a new unit of solving quadratic equations.  last week was mostly a review for the harder lessons we had this week.  in lesson 3.2 we started by solving quadratic equations by using the zero product law.

$x^2-6x+5=0$

$(x-1)(x-5)$

$x= 1, 5$

Verify :

$5^2-6(5)+5=0$

In lesson 3.3 we learned how to solve perfect square trinomials by completing the square.  remembering to put a plus and a minus symbol when adding a radical is an important step when solving and verifying.

$x^2+4x=2$

\$latex x^2+4x-2=0

$(x+2)^2-6=0$

$(x+2)^2=6$

$x=-2 \pm \sqrt{6}$

## Precalc week 5

This week in Precalc we finished unit 3 and started to review factoring for the upcoming unit, “quadratic equations”.  In lesson 3.1 we reviewed how to factor easy trinomials, difference of squares trinomials, hard trinomials and perfect square trinomials.  these are all important things to know for the upcoming units.

difference of squares:

$x^2-100$ $=(x-10)(x+10)$

easy trinomials :

$m^2+4m-45$ $=(m-5)(m+9)$

hard trinomials :

$5x^2+9x+4$ $=(5x+4)(x+1)$

perfect squares :

$9x^2+6x+1$ $=(3x+1)^2$

## Precalc week 4

This week in Precalc i was absent for the most part of the week so i only had two days of learning.   The most significant thing i learned was adding and subtracting radicals and defining variables.  Having the same radicand is only way to add and subtract radicals.  if the radicand is not the same then you must simplify the radical to find a common factor.

$2\sqrt{4x}$ $+4\sqrt{4x}=6 \sqrt{4x}$

x is greater than or equal to 0.

In lesson 2.4 we learned about dividing radicals.  You must rationalise the denominator by multiplying the top by the conjugate and then distribute and simplify.  Don’t forget to FOIL.

$5 \sqrt{5} - \sqrt{7 / }$ $5 \sqrt{3=}$ $3\sqrt{15} - \sqrt{21 / } 15$

In lesson 2.5 I learned about solving Radical equations.  I learned how to isolate a square root sign and determine the root of the equation and whether or not it’s a real root.  You can verify your answer by plugging x into the equation and checking to see if it matches.

$\sqrt{5x + 3} = \sqrt{3x +1}$

$2x = -2$

$x=-1$

It is not a real root

## Precalc 11 – Week 3

This week in Precalc we started unit 2.  We learned about an absolute value of a real number which is how far a number is from 0 and positive numbers always equal a positive number.

Ex :

|2| = 2

|-4|= 4

We also learned how to simplify radical expressions which was a good reminder on knowing how to simplify entire and mixed radicals.

Ex :

$\sqrt[3]{24x^3y^4}$

$2xy \sqrt[3]{3y}$

x and y are real numbers

## precalc 11 Week 2

This week in Precalc 11 we extended our unit to geometric sequences and series.  I learned more formulas and how to find the sum of a term.  we also learned infinite and finite geometric series which introduced the common ratio.

I discovered how to use the infinite geometric series formula to isolate the common ratio.  Multiplying each side by $1-r$ was not something I thought of.

## precalc week 2 arithmetic sequence with latex

arithmetic sequeunce : 6, 12, 18, 24, 30

$t_{n=}$ $t_{1+}$ $d$ $(n-1)$

$t_{50=}$ $6+6 (50-1)$

$t_{50=}$ $6 + 300 - 6$

$t_{50=300}$

FInd Tn :

$t_{n=}$ $t_{1+d}$ $(n-1)$

$t_{n=}$ $6 + 6 (n-1)$

$t_{n=}$ $6 + 6n - 6$

$t_{n=6n}$