## Pre-Calc Week #9

This week we learned how to do word problems with quadratic functions, like finding the maximum area of a certain amount of fencing or finding two integers with a sum or difference that have a minimum or maximum and find the answer to the maximum area or finding the two integers.

An example of how to find the integers is by taking, for example, x-y=15 and x*y=minimum and isolating one of the variables and using the substitution technique of turning it into x=y+16 and then replacing x in the multiplication with y+16 and solving before using the difference of squares to turn it into a quadratic and get an answer

Ex

## Pre-Calc 11 Week #8

This week in pre-calc we learned how to analyzing quadratic functions in the form of graphs using the equation

The vertex is found easily with this as the p variable is what ends up being the x value and the q variable being the y value in the vertex.

With the vertex we can then find the axis of symmetry.

With the coefficient of x (a being the variable of whatever the coefficient is) we can figure out if its maximum or minimum vertex if it’s negative or positive, if minimum it opens upward and if maximum it opens downwards. Using the information of the equation we can figure out what its congruent to as well as the rest of the information needed such as x/y intercepts and domain and range

## Pre-Calc 11 Week #7

This week I learned about the zero product law and how in a quadratic equation that = 0 we must make the x value be a opposite congruent of the other number in a factored binomial.

Basically after you have factored an equation and received an answer such as (x+2)(x+3)=0

The x value must be equal to the opposite of the number its adding to so the binomial equals 0

In that case the x would be equal to -2 so the -2 and +2 cancel out, the other x value would do the same with its binomial so it would be equal to -3 so the -3 and +3 cancel out and the equation = 0

In this example I will show how to do it from factoring to solving what x must be for it to equal 0

## Pre-Calc 11 Week #6

This week we learned how to use the quadratic formula and when we should.

In this example I show when we should use the quadratic formula (the first step is to find the discriminant using the formula in the example)

With a discriminant of +24 we know it has 2 roots

if the discriminant was 0 it would have 1 root and if it was negative it would have no root meaning it is unfactorable

In this next example I use the quadratic formula to find an exact answer

With this answer I can then simplify by simplifying the radical and then dividing by a common number in this case 2

## Pre-Calc 11 Week #5

This week in Pre-Calc 11 we started learning how to factor and simplify, we learned how to do this using Punnett Squares and using the acronym CDPEU to mean Common, Difference, Pattern, Easy and Ugly respectively. Using CDPEU means looking for what’s common, a difference of squares, a pattern within and if it’s easy or ugly In this example I show how it can be common or how it could be a difference of squares

In this next example I show how to simplify when it’s ugly

## Pre-Calc 11 Week #4

This week in pre-calc 11 we learned how to subtract and add radicals

the first step is to simplify the radical like example would be 2

no matter if the radical is mixed or entire for radicand must be the same

Example: You can’t add and

In this example I show how when the radicand is the same you can add them + = which equals 2

When the radicand is not the same you have to try to use prime factorization to give the radicand a coefficient which hopefully ends in a radical that has the same radicand

Radicals with coefficients add and subtract differently, in this example I show how to made entire radicals into mixed to give them coefficients to make the radicands equal and show that in subtracting and adding mixed radicals with the same radicand you add or subtract the coefficient.

Remember that radicals without a coefficient have a hidden coefficient of 1.

## Pre-Calc 11 Week #3

This week we learned about absolute values which is the non-negative value of a number or variable

In this example i show how 2 and -2 have the same absolute value of 2

This is true because the absolute value of -2 can’t be a negative, so it is also 2

There can also be absolute values of variables in which variables turn positive.

In this next example I will show how to do equations that include absolute values, where you have to use the equation as if they’re in brackets before putting whats not in the absolute value into the question after

## Pre-Calc 11 Week #2

This week I learned about finite geometric series and how to find the general term () along with how to find the sum of whatever the term number is.

To find , you need and the common ratio

In this example I’m looking for with a of 5 and a common ratio of 2

And in this next example I show how to find with the same numbers.

## Pre-Calc 11 Week #1

This week in Pre-Calc 11 we learned how to use the patterns in arithmetic sequences and series to find a number later in the series/sequence.

Basically if is 4 and is 8 we can tell the common difference is +4 using the common difference we can find any number after.

In this example I’ll show how to get using the information found