This week we started our final unit of precalc 11 which is Trigonometry.

we leaned the Sine law and the cos law

and CAST

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This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.

When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a prefect point, you will not be able to be completely accurate. To solve get everything equal to zero.

Example:

- y = x
^{2}– 5x + 7 - y = 2x + 1

Make both equations into “y=” format:

They are both in “y=” format, so Set them equal to each other

x^{2} – 5x + 7 = 2x + 1

Simplify into “= 0” format (like a standard Quadratic Equation)

Subtract 2x from both sides: x^{2} – 7x + 7 = 1

Subtract 1 from both sides: x^{2} – 7x + 6 = 0

Start with: x^{2} – 7x + 6 = 0

Rewrite -7x as -x-6x: x^{2} – x – 6x + 6 = 0

Then: x(x-1) – 6(x-1) = 0

Then: (x-1)(x-6) = 0

Which gives us the solutions x=1 and x=6

Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers

The matching y values are:

- for x=1: y = 2x+1 = 3
- for x=6: y = 2x+1 = 13

Our solution: the two points are (1,3) and (6,13)

This week in Pre Calculus 11 we learned about Graphing Linear Inequalities in two variables. The solutions to these inequalities are represented by a boundary line and shading one side of the line.

Ex:

key notes

choosing any coordinate (the easy one is 0,0) and seeing if the statement is true or false.

This week in pc we analyzed the quadratic function. In the equation each variable represents something that can change the graph.

positive sign, the graph moves up, negative sign, the graph moves down.

positive sign, the graph moves right, negative sign, the graph moves left.

positive sign, the graph opens up, negative sign, the graph opens down.

greater than 1, the graph is stretched vertically, between 0 and1,

the graph is compressed vertically.

This week we learned discriminants. A discriminant is a part of the quadratic formula and can determine the number of solutions in a quadratic equation without solving the equation.The solution(s) to a quadratic equation can be calculated using the **Quadratic Formula**:

The “±” means you need to do a plus AND a minus, so there are normally TWO solutions

The blue part (**b ^{2} – 4ac**) is called the “discriminant”, because it can “discriminate” between the possible types of answer. If it is positive, you will get two normal solutions (two real roots), if it is zero you get just ONE solution (one root), and if it is negative you get

that is what I learned from week 7