During this week I found some skills a little difficult, and wanted some extra practice on a few skills.
Some key points to remember:
general form: Y intercept/ Y= ax2 + bx +c = 0
Vertex: Vertex Point/ Y=a(x-b)2 +c
factored: X intercept y= a (x-b) (x-b)
For this example, I want to focus on general form quadratic equations, and converting these equations.
The function I chose to show is y=(x+3)2 – 9 which we put into general form which is y=ax2+bx+c.
I like to write out both equations again so I can cleary see them so I do not mix up a number or write it incorrectly.
You then re-write the equation in a longer form. So we square what is in the brackets so we can see it clearly.
Now I multiply where the arrows indicate, and write it out fully. Therefor, now I have 4 terms and the constant.
I now have to put the like terms together, so I take x2 with x2 which gives me 2×2. Same thing with 3x and 3x, therefor that gives me 6x.
Now my equation is in general form, and has all of the terms included.
Another step within quadratics that I found important was being able to identify the pattern and what direction you graph in.
For this example, i can already see that it is a negative so I know it will be a downwards angle instead of upwards. I can also tell it would start at zero on the graph because it has no vertex point within the function. These are a few ways I can identify and start to spot before doing any actual calculations.