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Week 12-Solving Absolute value Equations

This we learn how to solve the solution of the absolute value Equation

First we learned how to use the graph to solve

this question is asking that what’s the x solution are by looking the graph

we can see the equation

|-3x+3|=9

The y intercept is 3

So there two possible inside the absolute

First:-3x+3=9

-3x=6

x=-2

Second:-(-3x+3)=9

3x-3=9

3x=12

x=4

And because of when the y=9 touch the linear the x=-2,4

so the solution are -2,4.

EX:Another example is about the x square

Formula: $4+2x=|x^2 +8x+12|$

First possible

x is positive

(x+2)(x+4)=0

x=-2,x=-4

Second posible

x is negative

(x+2)(x+8)=0

x=-2,x=-8

Because absolute can’t be the negative.so when x=-4 ,x=-8

4+2x is negative , so they can’t be the solution of this,

so the solution is x=-2

By binerl2016 November 26, 2018. No Comments on Week 12-Solving Absolute value Equations Math 11, Uncategorized

Week 11-Graphing Linear inequalities in two Variables

PART 1:If you want to slove the graph is in which part of, you can use the test point

Ex:

3x-2y>(=)-16

Is (-3, 4) can be in this part?

so 3(-3)-2(4)>(=)-16

-9-8>(=)-16

-17>(=)-16

From there we can see this point can be the formula used

so if this point is outside, so you can draw the part inside(can be use), so if this point is inside, you can draw outside(can be use).

WARN:And don’t forgot if the formula have (=) the line should be the soild line, if there is no (
=),so the line should be the broken line!

PART 2:SOLVING SYSTEMS OF EQUATIONS GRAPHICALLY

we learn from grade 10

How much solution can linear system have?

There possible:1 , countless ,no

And we leaned the possible of two quadratic functions

one, two and none

two solution is the max

same with the linear function with the quadratic function

(use the desmos if you can’t see the solutions(the point or points that they meet)

By binerl2016 November 18, 2018. No Comments on Week 11-Graphing Linear inequalities in two Variables Math 11, Uncategorized

Week 10-solving Quadratic inequalities in one variable

The formula that we learned

$ax^2 +bx+c<0$ $ax^2 +bx+c>0$ $ax^2 +bx+c<(=)0$ $ax^2 +bx+c>(=)0$

where a, b, and c are constants and a not =0

Ex:

The solution of the quadratic inequality

$x^2 -2x-3>0$ is the value of x for which y>0 ; that is ,the values of x for which the graph is above the x -axis.Visualize the shadow of the graph on the x-axis.

so we first have to factor this formula

$x^2 -2x-3=0$

(x-3)(x+1)=0

ok, so we can get the value of x for equal to zero

x=3,x=-1

and because y>0

so the part of y>0 are

-1>x>3

By binerl2016 November 11, 2018. No Comments on Week 10-solving Quadratic inequalities in one variable Math 11, Uncategorized

Week 9-Modelling and Solving Problems with Quadratic Functions

This week we learned three formula form

General Form : $y=ax^2+bx+c$

Standard Form(Vertex form:Ms.Burton’s Favorite): $y=a(x-p)^2 +q$

X point form(x intercept form):y=(x-x_1)(x-x_2)

Ex:the rectangular have the area is to be bounded by 120 m of fencing(determine max area)

so we can get two formula

2L+2W=120

L*W=mix

so we can use the first formula get this form

L+W=60

L=60-W

SO PUT THIS FORMULA INTO THE SECOND FORMULA

(60-W)*W=MIX

We can get

$-(w-30)^2 +900=MIX$

So the vertex is (30,900):the 30 m is the w , and the $900 m^2$ is the MIX area

so we can use the formula L=60-W ,to get the L=30

so it is a square .the special rectangular

By binerl2016 November 4, 2018. No Comments on Week 9-Modelling and Solving Problems with Quadratic Functions Math 11, Uncategorized

week 8-Analyzing Quadratic Functions of form

A quadratic function is any function that can be written in the form $y=ax^2+bx+c$ , where a, b ,and c=R and a didn’t =0.

This is called the general form of the equation of a quadratic function.

The graph of ever quadratic function is a curve called a parabola.

The vertex of a parabola is its highest or lowest point . the vertex may be a minimum point or a maximum point.

The axis of symmetry intersects the parabola at the vertex.The parabola is symmetrical about this line.

The X-intercept is mean the points that when the parabola touch the horizontal line and the Y-intercept is mean the points that when the parabola touch the vertical line.

Analyzing quadratic functions of the form:

$y=x^2$ is the parents function,

The vertex is (0,0)， X-intercept is (0,0),Y-Intercept is (0,0)

We learned a new one: $Y =x^2+R$

This R is a positive number, if this number change to the more and more big, it will make the parents function goes up (+R),and the vertex goes up too.

The second one is : $y=x^2-R$

This R is a positive number,if this number change to the more and more small, it will make the parents function goes down(-R),and the vertex goes down too.

The third one is $y=ax^2$ , |a|>0

when |a|>1, the parabola will be more and more skinnier with the ‘a’number goes more and more big,

when |a|<1,the parabola will be more and more compression with the number goes more and more small.

WARN: If the “a” is a negative number the parabola opens down, if the “a “is a positive number , the parabola opens up

The fourth function is $y=(x+R)^2$

The R is a positive number, so the size of this number is the distance to the left the parents function

The fifth function is $y=(x-R)^2$

The R is a negative number, the size of this number is the distance to the right the parents function

THANK YOU FOR READING, HOPE YOU LEARN MANY FROM MY BLOG POST!

By binerl2016 October 28, 2018. No Comments on week 8-Analyzing Quadratic Functions of form Math 11, Uncategorized

Week 7-review

This week we did the review and skill check for the test

The important thing that we learned was discriminant:

$b^2-4ac=0$

There are one solution(2 equal solutions)

$b^2-4ac>0$

There are two distinct(unequal)solutions

$latex b^2-4ac<0$

There are no roots.

look the picture

By binerl2016 October 23, 2018. No Comments on Week 7-review Math 11, Uncategorized

Week 6——Developing and Applying the Quadratic Formula

use the way that we learned to make ax²+bx+c=0 change to

$\frac{-b+-\sqrt{b^2-4ac}}{2a}$

Ex:

x^2+9x -2=0

use the formula that we just make

a=1，b=9，c=-2

$\frac{-9+-\sqrt{9^2-4\cdot1\cdot-2}}{2\cdot1}$ $\frac{-9+-\sqrt{81+8}}{2}$ $\frac{-9+-\sqrt{89}}{2}$

finished

so we can use this formula to solve the question easily and correctly

By binerl2016 October 16, 2018. No Comments on Week 6——Developing and Applying the Quadratic Formula Math 11, Uncategorized

Week 5-Radical Equations

Add the square root of the same coefficient

ex: 1-3√5x=-3-2√5x

-3√5x+2√5x=-3-1

-√5x=-4

Than use the way that square both sides of this to get rid of the square root

5x=16

x=16/5

Review

$\frac{2\sqrt{6}}{\sqrt{7}+\sqrt{5}}$

[Than multiply both the top and the bottom by a number , which is goodfor removing the square root of the denominator(( $\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$ =3-2=1)]

= $\frac{2\sqrt{6}(\sqrt{7}-\sqrt{5})}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})}$

= $\frac{2\sqrt{42}-2\sqrt{30}}{7-5}$

= $\frac{2\sqrt{42}-2\sqrt{30}}{2}$

= $\sqrt{42}-\sqrt{30}$

By binerl2016 October 11, 2018. No Comments on Week 5-Radical Equations Math 11, Uncategorized

Week 4 -Adding and subtracting radical expressions

When you simplify your radicals down, you can only add common radicals together. When you’re adding or subtracting radicals, the radicand always stays the same, which is why you need to have a common radicand. Once you’ve collected common radicals you you either add or subtract the co-efficients together depending on the sign

EX:3√5+6√5（They have same radicand）=9√5

We also learned how to make it simplify

You have to simplify the number in the root as much as you can by multiplying it by several equal numbers

EX:square root：√64=√4*4*4=4√4

cube root： ³ √81=³√3*3*3*3=3 ³√3

it makes you can better to add up some numbers with the root

see the picture

By binerl2016 October 4, 2018. No Comments on Week 4 -Adding and subtracting radical expressions Math 11, Uncategorized

Week 3 Absolute Value and Radicals

√25=5

The absolute value of a real number is defined as the principal square root(√25) of the square of a number.

EX:|9|=3 ,|-9|=3

√9²=√81=9=|9|=|-9|

√（-9）²=√81=9=|9|=|-9|

Simplifying Radical Expressions

Coefficient√Radicand

Square roots :ex ²√16=4

Roots(-other roots)[

Cube roots :ex³√27=3

Warn：²√x （x≥0）restriction

³√x （x∈R）restriction

By binerl2016 October 3, 2018. No Comments on Week 3 Absolute Value and Radicals Math 11, Uncategorized