Quadratic Curves - Math

 Oh my god!! This is the third post today but it's all the compensation for the missed posts ever since December.
Today, we will be discussing something different than what we usually do and that is MATH! I can't believe that we have been blogging for so long and haven't done math ever, so here you go, our very first math post around here.

We will go through a complicating topic that is honestly not too complicating once you get the hang of it so let's get into it!

When we get a question like this one and they order us to sketch a quadratic curve, we do the following:

Step 1, We substitute y with 0.

Why? Because we need a values that are on the x axis (x , 0), so we replace y with 0.

Now we do a process of factorisation called the "sum and product" which requires us to do the following:

1. Get a factor pair of 10 that adds/subtracts to 7 from 7x

2. In this example 2 * 5 = 10 and 5 + 2 = 7 so this is perfect

3. Now we split x^2 into two brackets:

To get the value of x we need to make x the subject of the formula in the following equations:

Now these are our coordinates for the graph:

We have successfully completed the First Step of our 3 step procedure.

Step 2 we substitute x = 0

Why? Because we need a values that are on the y axis (0 , y), so we replace x with 0.

There goes without doubt that once a number is multiplied by 0, the product is 0 and now we can completely eliminate x out of the equation.

We've gotten our coordinates for y!

We have successfully made it through the easiest step. (sorry step 3 is the hardest, just hold your confetti for when you are done.)

Step 3 we complete the square and find the vertex

Have you seen this equation before? Well, this is the equation we will be fitting our previous equation into.

a^2 = x^2

2ab = 7x

b^2 = (7/2)^2

Why do we subtract  (7/2)^2? 

This is because  (7/2)^2 isn't really a part of the orignal equation and is an addition to it and so we must remove it.

We divide 7/2 and are left with 3.5 and put it inside a bracket with x and square it. 
We Square the other 7/2  and get - 49/4

Basically, 10 = 10/1 and so we make it stand up on 1 and make its denominater same by multiplying it by 4.

Now we add it up and get -9/4. 

We shove these values into coordinates and there!

Since 3.5 has to be reperesented as -p we will make it negative. 

AAAND FINALLY!! WE HAVE MADE IT PAST THE TRICKIER ONE!! 

But wait, keep your confetti down still, scroll to the top and realize that you were meant to sketch it, pull your graph paper out and plot your coordinates.

I did say we have 3 steps but we have another one and, yes, I can clarify not calling it a step - its super easy and you'll be done in a jiffy. Actually it is an important step please don't forget it. 

Plot the coordinates and connect all of the dots together.

Now avert your eyes from the screen and plot down your coordinates before you look at my graph.

Here it is! Did you get it right? If you did lets pop the confetti and give yourself a pat on the back. 
Always remember, it might be hard at first but the more you try you're going to get it.

PDF Step By Step 

Graph Answer

Until next time, 

rock on,

er, math on,

Nab.