I have talked about the 3 main representations of a quadratic equation and each of its significance previously.
Today, I am using a real examination question to illustrate on The Completed Square Form and its significance.
sketch
What Is The Difference Between Sketch And Draw?
It is important to know the difference between Sketch A Graph & Draw A Graph.
Sketch ==>
- On foolscap paper
- Best Representation of the graph
- Less time as it reflects only the general shape of the graph.
Draw ==>
- On graph paper
- Accurate representation of the graph
- More time needed as it usually involves more points on the graph
- Curve rule/french curve is usually required.
Example:
Sketch
What I will do :
- Find x-intercept (i.e. set y = 0)
- Find y-intercept (i.e. set x = 0) y = 1
- Put the 2 points on the axes I have drawn on foolscap, join the 2 points, label the line.
Draw
- Set up a table of 3 values of x choosen randomly i.e x = -1 , 0, 1
- Find out values of y for each value of x by substituting into the equation of the line.
- Plot the points on a graph paper accurately.
- Join the 3 points, label the line.
Good in straight line? You might want to check out how you can draw Exponential Graph here even with NO Math knowledge.
What Has My Left Palm Got To Do With Math?
Palm Reading for my Destiny? Nope.
I was recently doing graph topics with some students. And some were complaining how much they have to memorize until I revealed to them some of the Underground Secrets on Mastery Of Graphs. They were amazed and amused.
Click on pictures for clearer view
Our palms have the exponential graph embedded on them! Now you have 1 less graph to take care of. Just ensure you keep your hands nice and clean so that the palm lines stay on for you forever.
When the need to draw arises, flip that palm up :)
Warning: You ought to do it tactfully in case the invilgator suspects you of cheating. Haha
I will be writing on more secrets on Mastery of Graphs. If you like these secrets, subscribe to singaporeolevelmaths for free to be posted of more updates.
A-Math More Trigo Graphs
Another question for O Level Additional Mathematics (A-Math).
On the same diagram, sketch the graphs of
y=sin 3x & y=cos2x,
for x between 0 degree and 180 degree
Hence state the number of soutions to the equation
sin 3x=cos 2x
in the interval 0 degree less than or equals to x which is less then or equals to 180 degree
Click on image to have a larger view
Drawing of Trigo Graphs
Can you give an example of a drawing of tangent graphs? For eg, 3tan2x + 1, what does each stand for and how do i go about drawing?
From the drawing, you see only 1 diagram instead of a few diagrams as what most people will have.
The secret is............ I drew my x and y axis LAST which is the reason why my diagram is so neat and it takes me less than 2 min to complete : )
Click on diagram to have an larger view
