Unit 2: Curve Sketching (Chapter 4, 6, 8)

What is curve sketching?
Curve sketching can be make in accurate sketch of lots of function using the concepts.

Chapter 4 (Number Plane Graphs and Coordinate Geometry)
4:01 Parabola
Most graphs are straight line but this is mathematical curve called the parabola.
The parabola equations are called quadratic equations and have x2 as the highest power of x.
But this is the simplest equation: y = x2

Here is one of the exercise I solved:
a) Complete the following tables and then graph all four curves on one number plane. (On the y-axis, use values from -2 to 13.

-> y = x2

x	-3	-2	-1	0	1	2	3
y	9	4	1	0	1	4	9

4:02 (Parabolas of the Form y = ax2 + bx + c 

It says that all parabolas have the same basic shape.

The connection between the parabola's shape and its equation and at what numbers in the equation influenced the steepness of it.

4:03 (The Hyperbola)

We need to take many points when graphing a curve like y = 2/x, as it has two separate parts. The equation is called a hyperbola. 

This is one of the example of how to solve the problem

x	-4	-3	-2	-1	-0.5	0	0.05	1	2	3	4
y	-0.5	-0.7	-1	-2	-4	-	4	2	1	0.7	0.5

So the as you can see there is no value for x = 0. because when x = 0, y = 2/x becomes y = 2/0. 

This value cannot exist as no number can be divided by 0. 

Chapter 6 (Curve Sketching)

6:01 Curves of the Form y = axn and y = axn + d

The method used to graph a curve has relied on using the equation of the curve to produce a table of values. This gave a set of points on the curve, which this could be plotted. This procedure is basic to curve sketching. It's the only way to producing an accurate graph of a curve.

When it's impossible to draw a right graph, a sketch is being made.

This is one of the curve sketch example

and here is one of the example of how to do the problem

1. y = -2(x - 4)(x - 4)(x + 2)

answer:
1. the curve has x-intercepts x = 1
    we need to consider the size of y when x is bigger than 4 and less than -2 gives the correct shape.