on 6.1 Angles in Standard Position in Quadrant 1
SOH CAH TOA
Sin Cosin Opposite
Adjacent Opposite Opposite
Hypotenuse Hypotenuse Adjacent
The Triangular ratio is work in only a right triangle.
Terminal arm is the line that the (0,0) to (r cos@, r sin@)
Terminal point is (r cos@, r sin@)
on 7.3 Adding and Subtracting Rational Expressions with Monomial Denominators.
Add or subtract. State the restrictions on the variables.
compare the strategies you used with those for adding and subtracting rational numbers.
Ex) {7(x+7)+3(x-7)} / (x+7)(x+7)(x-7) = (10) / (x+7)
[{(x+2)(x-5)} / 3x(x-5)] – [2(3x) / 3x(x-5)] ==> (x+2)(x-5)-6x / 3x(x-5) = (x+2)-2 / 3x(x-5)
on Equivalent Rational Expressions
A rational expression is an algebraic expression that can be written as the quotient of two polynomials.
Rational expressions are not defined for values of variable that make the denominator 0. These values are called
non-permissible values.
Ex)5𝑥−2
4𝑥−16
non-permissible value is x is not 4
on Solving Absolute Value Equations
This is the graph of y=|2x^2-4|
Ex)y=2x^2-4 ,
y=-2x^2+4
If you absolute Values the equation, you need to put – sine
infront of the absolute value equation.
on Absolute Value Functions
Construct Understanding
Complete the table below to graph the functions y=x and y=|x|.
Compare graphs in as many ways as you.
Ex)y=|-x+4|
x 0 2 4 6 8
y=-x+4 4 2 0 -2 -4
y=|-x+4| 4 2 0 2 4
An absolute value function has the form y=|f(x)|, where f(x) is a function.
on Solving Systems of Equations Graphically
If the graph is parallel, should be no solution
If the graph is overlap, it should be infinite solution
If the graph is verticality, it should be 1 solution
Ex) y= (75+10x)(20-x)
y= 1000 + 75x
on Solving Quadratic Inequalities in One Variable
Quadratic inequality in one variable can written in general form as:
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 in include 0.
on Equivalent forms of the quadratic function
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape. The picture below shows three graphs, and they are all parabolas.
Ex)
y = x2 + 8x + 16
= (x+4)2
:vertex(-4,0)
y-int= 0
x-int=-4
on Analyzing Quadratic Functions of the Form
y=a(x-p)^2+q
The Effect of Changing p in y=(x-p)^2
If p values is > 0 : translate p units left from y=x^2
If p values is < 0 : translate p units right from y=x^2
The Effect of Changing q in y=x^2 + q
If q values is > 0 : translate q unites up from y=x^2
If q values is < 0 : translate q unites down from y=x^2
The Effect of Changing a in y=ax^2
If a values is > 0 : Stretch a unites from y=x^2
If a values is < 0 : Compression a unites from y=x^2
Ex)
y=(x-2)^2 + 42
Translate 2 unites left and Translate 42 unites up.
on Interpreting the Discriminant
Using the “Quadratic Formula”, we can count how many solutions are there.
If b2−4ac>0, the equation has two separate real solutions.
If b2−4ac<0, the equation has only non-real solutions.
If b2−4ac=0, the equation has one real solution, a double root.
Ex) x2+4x+4=0
16-16=0 so this one real solution.