Math 10C Pre-IB Portfolio Assignment Type 1 Investigating the Quadratic Function
A quadratic function is one where the highest exponent of the independent variable is 2. The quadratic function can be written in the general form of, where a, b, and c are real numbers. However, the quadratic function can also be written in the standard form of , which is sometimes more preferred, where p and q are the x and y coordinates of the vertex, respectively.

The purpose of this task is to investigate the graph of a quadratic equation, the parabola, when the equation is written in the form. By analyzing p and q we can determine the vertex of the graph. Also, by increasing or decreasing the values of p or q, we can translate the parabola vertically and/or horizontally.

First, if we look at the functions y=x2 ,y=x2+3, y=x2-2 we know that all 3 are in general form. To convert general to standard form you will need to use the process called “completing the square” which goes as following: Ex.

y=ax+bx+c

Now if we convert the three functions mentioned above, in standard form respectively they are y=x020, y=x02+3 and y=x02-2. Now if we were to graph these points, either the standard or general form would work.

y=x2 , y=x020 y=x2+3 , y=x02+3

y=x2-2 , y=x02-2

Other examples of these types of graphs could be anything along the line of. An example of a parabola in the form of y=x2q with either a positive or negative q value could be y=x2+5 and y=x2-4. When we graph the two equations they are as...

...Rahul Chacko
IB Mathematics HL Revision – Step One
Chapter 1.1 – Arithmetic sequences and series; sum of finite arithmetic series; geometric
sequences and series; sum of finite and infinite geometric series. Sigma notation.
Arithmetic Sequences
Definition: An arithmetic sequence is a sequence in which each term differs from the
previous one by the same fixed number:
{un} is arithmetic if and only if u n 1 u n d .
Information Booklet
u n u1 n 1d...

...Grade 10 Academic Mathematics
Ontario Canada Curriculum MathWiz Practice Exam 1
Instructions: Provide solutions where needed with a final statement Pay attention to degree of accuracy required Check your work when finished
Part A
1. 2. 3.
Place your answers only in the space provided. Answers
Determine the slope of the line 3 x 2 y 8 0 . Determine the equation of the vertical line passing through A (5, 11). Determine the distance between the points X...

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also...

...the numerators the same.
Row Number (n) | Numerator in Each Row (N) |
1 | 1 |
2 | 3 |
3 | 6 |
4 | 10 |
5 | 15 |
From this table, I can see that the numerator is the result of the current row number added to the numerator of the previous row. That is, if you’re looking for the numerator of row 4, take that number and add the numerator from row 3, which is 6. 4+6=10, and 10 is the numerator of row 4, as shown in the table above. Knowing...

...Math Exam Notes
Unit 1
The Method of Substitution
-Solving a linear system by substituting for one variable from one equation into the other equation
-To solve a linear system by substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable
Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable
Step 3: Substitute back into one of the original equations to find the value of the...

...Math Studies: Units Project
Talha Mirza
1A Gilmartin
Dear noble tribe leaders of T-Island, I have created a brand-new system of units for us to use in our daily lives called the T-Dog system. You will find this system to be quite useful, as it includes six unique units which measure temperature, length, time, weight/mass, volume/displacement, and currency. By utilizing these units, life will be made easier for us. Moreover, if it is ever decided to switch to other...

...Jonghyun Choe
March 25 2011
MathIB SL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 1
1 1
Row 2...