Category: Grade 11

week 8-Analyzing Quadratic Functions of form

A quadratic function is any function that can be written in the form , 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:

is the parents function,

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

We learned a new one:

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 :

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 , |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

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

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!

 

 

 

 

Week 7-review

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

The important thing that we learned was discriminant:

There are one solution(2 equal solutions)

There are two distinct(unequal)solutions

$latex b^2-4ac<0$

There are no roots.

look the picture

Week 6——Developing and Applying the Quadratic Formula

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

Ex:

x^2+9x -2=0

use the formula that we just make

a=1，b=9，c=-2

finished

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

 

 

 

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

 

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