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The things that i learnt this week are angles in standard position in quadrant 1, angles in standard position in all quadrants, the sine law, the cosine law.
s=o/h c=a/h t=o/a
SOH CAH TOA
(cos0)^+(sin0)^=1 cos^+sin^0=1
for any angle 0 in standard position, where 0=<0=<360, with terminal point P(x,y), the primary trigonometric ratios are defined as: cos0=x/y
sin0=y/r
tan0=y/x
In any ABC c^=a^+b^-2ab cos C
For any ABC a/sinA=b/sinB=c/sinc and sinA/a = sinB/b =sinc/c
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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:Graphing Reciprocal and equivalent rational expressions.
that a rational number is a quotient of two integers (ex, -2/5) so the quotient of two polynomials is called a rational expression
factoring Trinomials Different of squares ex: x^-9=(x+3)(x-3)
each valve is the same (equivale for the 2 vational expressions)
These are equivalent forms of a rational expression. to reduce a rational expression, first factor the numberator and denominator then cancel out common factors
Find the non permissible valves before reducing otherwise you might miss some
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 learnt this week are: Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, Graphing Quadratic Inequalities in Two Variables.
Quadratic Inequalities is One Variable is in quadratic equation have equals sigh replaced with an inequality sigh, this is quadratic inequality in one variable.
A quadratic inequality in one variable can be written in general form as:
ax^+bx+c<0 ax^+bx+c<=0
ax^+bx+c>0 ax^+bx+c>=0
where a,b and c are constants and a not=0
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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.
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the thing that I learned this week are: analyzing quadratic functions of the form y=a(x-p)^2+p and equivalent forms of the equation of a quadratic function.
The effect of changing q in y = x^2+q
The graph of y=x^2+q is the image of the graph of =x^2 after a vertical translation of q units. when q is positive sigh the graph moves up, when the q is negative sigh the graph moves down.
The effect of changing p in y=(x-p)^2′
The graph of y=(x-p)2 is the image of the graph of y=x2 after a horizontal translation of p units. when p is negative sigh the graph moves right when p is positive sigh the graph moves left.
The effect of changing a in y=ax^2
the a greater then 1, the graph is stretched vertically. the a between 0 n 1 the graph is compressed vertically. a less then -1 the graph is stretched vertically and reflected in the x-axis. a between -1 and 0 the graph is compressed vertically and reflected in the x-axis.
Axis of symmetry: x=p
Vertex(p,q)
congruent to y = ax^2
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The thing that I learned this week are Solving Quadratic Equations by Factoring, Using Square Roots to Solve Quadratic Equations and Developing and Applying the Quadratic Formula.、
x^2-2x-8=0 contains a quadratic or second degree term, a term with a variable that is squared and no higher degree term, such an equation is called a quadratic equation.
That is, if ab=0, then a = 0 or b = 0 or a = b = 0.
This is called the zero product property.
When the Discriminant (b2−4ac) is:
How to solve it:
We can Factor the Quadratic
Or we can Complete the Square
Or we can use the special Quadratic Formula