Week 17 – Precalculus 11 – “Top 5 Things I Learned in Precalculus 11”

The top 5 things I learned in Precalculus 11 are: 

1. Solving Quadratic Equations by Factoring

2. Graphing Quadratic Equations

3. Parts of a Parabola

4. Operations with Rational Fractions

5. Sine and Cosine Law

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1. Solving Quadratic Equations by Factoring

Let’s say we have  x² +5x -14

What two numbers add up to 5x, but multiply up to -14?

7 – 2 = 5         7 x -2 = -14

(x+7) (x-2)

Learning how to factor quadratic equations was important for me to learn, because in later units, it is essential to know how to factor equations. So that is why it is important to me.

2. Graphing Quadratic Equations

Graphing quadratic equations was important to learn, because it is a visual way of understanding quadratic equations. From general form to vertex form, we know how our parabola will look like. 

These are parent functions:

The Y- value goes up 1,3,5,7,9…

The X-value goes up -3,-2,-1,0,1,2,3…

The stretch shows how narrow or wide your parabola will be:

3. Parts of a Parabola

Learning the parts of a parabola was important to learn, because we get to understand the information about our parabola. The vertex, LOS (Line of Symmetry), Minimum or Maximum, Opens up or Down, X-Intercept, Y-Intercept, Domain and Range are all the information we can gather from a parabola.

The vertex is the point where our parabola shoots back up. The line of symmetry is where our parabola is split in half. The minimum or maximum are two points where either the vertex is at the top, or at the bottom. Depending on if our parabola is a minimum or maximum, then parabola will either open up or open down. If it is maximum it will open down, and if it is minimum it will open up. X intercepts are where the parabola hits the x axis, and the y intercept is where the parabola hits our y axis. Domain is the x values that our parabola covers, and the range are all the y value that our parabola covers.

4. Operations with Rational Fractions

Operations with rational fractions is an important skill to learn because it will be be needed for future math classes.

Key things to know when adding and subtracting, is that we always have to have a common denominator. We cannot cross simplify because that law only applies to multiplying and dividing. When we multiply and divide, we must first look for terms that we can factor. When dividing, we turn our equation into a multiplication statement, then cross simplify, then multiply. To multiply, we just go ahead and multiply, but first we must look for quadratic terms we can simplify, then we look for terms we can cross simplify, then finally multiply.

5. Sine and Cosine Law

Sine and cosine laws were important to learn, because if we need to find missing information from our triangle, we can use either of the laws.

This is the formula for sine law.

Here are the formulas for cosine law:

Sine law is used to determine side lengths or angles in a triangle. We need 2 side lengths and one non-contained angle, or 2 angles and a side length. 

Cosine law is used to determine an angle when all 3 side lengths are given, or to find a missing side length when two sides and a contained angle are given.