This week we learned how to solve the unknown value from the score formula
Then we make all the term time common denominator
so we get the common denominator is 4v
Then we learn how to solve the unknow number in the life things
So we make Mary need x hours to finish , her apprentice need x+9 hours to finish
And if they do together , so they will finish in 20 hours
so we know after 1 hour Mary finished , her apprentice finished
so we got a function that are after 20 hours
+=1(this ‘1’ is mean 20 over 20)
And you use the way that times common denominator
then we factor
we get (x-36)(x+5)=0
And we get 36 ,-5
but -5 is not belong to the question
so we just get 36 is mary
than we get 36+9=45 is her apprentice
This week we learned how to make a function simply
we need to factor first
we can see the same thing from the top and the bottom, so we can get rid of them
so it is (x+3)
After that we can get
Next step we have to make sure the range of values of “x” and what number can’t it become,
First we can see this formula: for values of bottom can’t be “0”
“x “can’t be -3 and -5
second we can see this formula : ,in the bottom x can’t be -5
WARNING : you have to check the all function , even the first one ,one special is start by diving by a fraction , and then you have to multiply by the inverse of that fraction , and you have to look at the denominator of that fraction to make sure that the unknow numbers before and after reciprocal and which number can’t be.(“0″ CAN’T BE THE BOTTOM”)
This week we learned reciprocal quadratic functions graph
So when we get the function, we have to graph the (parent function)quadratic formula first ,and then we have to find the invariant points ,which is when y=1 . y=-1 ,the points that on the parent function graph ,we can see this picture don’t have find the vertical asymptotes ,so there is no vertical asymptotes, because the x=0 is the asymptotes already so we don’t have to draw another one ,just have the horizontal asymptotes y=0 (in this term we just earn y=0)
First we also we have draw the parent formula, and there is no invariant point.we can find the reciprocal of number in the end (2) to find a point that the reciprocal of the quadratic function touch in the y line(x=0)
Ok so we draw the parent function again , find the x-intercept to find the vertical asymptotes (two) ,and there have the four invariant numbers ,and for the third graph line that function of the reciprocal of the quadratic function ,you also can find the point that reciprocal of the end number (four to be one over four:0.25) that where it touch at the y line(x=0)
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
The y intercept is 3
So there two possible inside the absolute
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
x is positive
x is negative
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
PART 1:If you want to slove the graph is in which part of, you can use the test point
Is (-3, 4) can be in this part?
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)
The formula that we learned
where a, b, and c are constants and a not =0
The solution of the quadratic inequality
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
ok, so we can get the value of x for equal to zero
and because y>0
so the part of y>0 are
This week we learned three formula form
General Form :
Standard Form(Vertex form:Ms.Burton’s Favorite):
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
so we can use the first formula get this form
SO PUT THIS FORMULA INTO THE SECOND FORMULA
We can get
So the vertex is (30,900):the 30 m is the w , and the 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
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!
use the way that we learned to make ax²+bx+c=0 change to
use the formula that we just make
so we can use this formula to solve the question easily and correctly