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The things that learnt this week are Multiplying and dividing rational expressions, Addition and subtraction of rational expressions, Addition/Subtraction with “ugly” denominators.

The strategies for multiplying and dividing rational numbers can be uesd to multiply and divide rational expressions. All non-permissible values of each expression being multiplied or divided must be stated.

how to solve it:

Divide the numerators and denominators by their common factors. Multiply the numerators. Multiply the denominators.

Since division by 0 is not permitted, any value that makes the numerator of the divisor 0 is a non-permissible value.

When the polynomial in numerator or denominator is a binomial or trinomial, it may be factored before simplifying the expression.

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The things that i learnt this week are: Absolute Value Functions and solving absolute value equations.

An absolute value function has the form y=|f(x)|, where f(x) is a function. The x-intercept of the graph of y=f（x）is a critical point. The graph of y=|f（x）| changes direction at this point..

Graph the absolute value of a linear function we should know the intercepts, domain, the range of the function. To see how to join the points with a smooth curve, sketch the graph of the quadratic function then reflect, in the x-axis, in the part that is below the x-axis.

Piecewise notation is used to describe  a function that was different definitions for different subsets of the domain.

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The thing that i leant this week are: solving systems of equation graphically,  solving systems of equations algebraically

systems is when 2 or more equations are needed to final a solution.

The equation of a linear function and the equation of a quadratic function from a linear-quadratic system of equations

The coordinates of a point of intersection of the graphs of the equations in a system are a solution of the system.

The equations of two quadratic functions form a quadratic-quadratic system of equations.

a solution of a linear-quadratic system of equations is an ordered pair,(x,y),that satisfies both equations in the system. The system may have 0,1,or2 solutions.

A solution of a quadratic-quadratic system of equations is an ordered pair that satisfies both equations in the system. The system may have0,1,2,or infinite solution.

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The thing that I think are difficult are  arithmetic sequence, solve radical equations, solve quadratic equations.

In an arithmetic sequence, the difference between consecutive terms is constant. This constant value is called the common difference. The General Term of an Arithmetic Sequence is :tn = t1 + d( n – 1 )

how to solve radical equations.

Step:
1.Isolate the radical
2.Square both sides
3.Solve for X
4.Check for Extraneous roots by substituting.

how to solve quadratic equations

We can Factor the Quadratic

Or we can Complete the Square

Or we can use the special Quadratic Formula

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the thing that I learned this weekend is Modelling with quadratic equations.

we should focus on Writing a quadratic function to model to a problem, then solve the problem.

We should determining maximum or minimum related to operations with numbers.

We can list the table and draw the graph for solve the problems.

The opening direction is only related to the quadratic coefficient, greater than zero opening upward, less than zero opening downward.