### November 2019 archive

At the beginning of this week in pre calc 11 we learned about Vertex/Standard form. This is personally my favourite form because it provides more information about us graphing the quadratic function than the quadratic or factored forms give us.

Vertex/Standard form looks like this: $y=a(x-p)^2+q$

This form provides you with the following information about a parabola:

a:

1- tells us whether a parabola is opening up or down. If it’s a positive # than it’s opening up, and if it’s a negative # than it’s opening down or being “reflected”.

2- determines the size of our parabola, whether it is stretched or compressed. If a is greater than one then the parabola is stretched, if a is less than one then the parabola is compressed.

p:

1- tells us the horizontal translation of a parabola (whether the vertex is moving left or right).

2 – tells us what our line of symmetry is.

q:

1- tells us the vertical translation of a parabola (whether the vertex is moving up or down).

p & q:

1- the p and q are very important becuase they let us know our vertex *the vertex is the most important part of any parabola. The p tells us our x co-ordinate and the q tells us our y co-ordinate for when we are graphing a quadratic function.

This week in pre calc 11 we started chapter 4, and the first thing we learned was properties of quadratic functions. Now it’s important that before we start listing off the properties of each of these quadratic functions, that we know 100% that this is a quadratic equation. How can we tell if a function is linear, quadratic, or neither. In this blogpost I’m going to show you how you can tell the difference between a quadratic function and a linear function by looking at the table of values for any type of function.

Linear – look at the first differences, if they are equal to each other than it is a linear function.

Quadratic – Look at the second differences, if they are equal to each other than it is a quadratic function.

Neither – Than it just simply doesn’t follow any of the rules from above and is not a linear or quadratic function.

Ok so lets begin, suppose we have this table given to us: The first step is to find the first difference, how you do this is to find how much space is between each of the #s. As you can see, the first differences are equal to each other therefor this is a linear function.

Let’s look at another example: Follow the same steps as you did for the function above: As you can see, the first differences aren’t equal to each other so now we have to find the second differences: The second differences are equal! Therefor this is a quadratic function.

Lets look at one last example: First – find the first differences: The first differences aren’t equal so we move on to step 2 – finding the second differences: For this example both the first and second differences are not equal therefor this is neither a quadratic or linear function.

This week in pre – calc 11 we learned chapter 2.6 – solving equations algebraically. One thing that stood out to me was learning how to rationalize the denominator to solve an equation that looks like this one: The first step is to multiply the $\sqrt{3}$ “rationalize” it. The $\sqrt{3}$ multiplies with everything and cancels out the $\sqrt{3}$ on the bottom of the equation. The next step would be to further simplify but as we can see we no longer can simply this equation further, so we leave it like this

Here is an example of an equation which also requires to be rationialized, take a couple seconds and try to solve this using what you know about rationalization: Below is the answer and me solving this equation using rationalization: 