Graphs- Curve sketching

During class we improved our skills on identifying curves and then sketching them. To start off the lesson we looked at a simple linear equation (y=mx+c) and finding out how to get the Y intercept, X intercept, and gradient. Afterwards we then see what would happen if we made y or x infinity.

Afterwards we got 3 equations to sketch graphs for.

y=5+x

y=x^3-1

y= (x+1)/(x^2)-3)

Maximum Area and we taught trig.

Research Question: What is the biggest area that you can enclose with a perimeter of 24cm.


To attack the question first I looked at it at the most basic form. I made different rectangles with different lengths and widths from a thin rectangle up to  a square then find their areas.

Formula of perimeter: 2x+2y=perimeter x.y=area

Then we realized that by having the x and y closer together the bigger the area is. Afterwards i went wait. what if I go for a circle since the shape has infinite edges therefore having more space from the edges.

So we went from the circle. Formula of the area is πr^2. By have a circumference of 24 the radius would be 24/2/π = 12/π = 3.8197 then put it into equation which means π3.8197^2=45.8

This therefore makes it the biggest area you can get from a 24cm perimeter. By using the

information from the rectangles we know that the more flattened the shape is, it also has less area
meaning that an oval would have less area than the circle. Also using a triangle or any other shape
with a countable number of edges would also have less area that a circle because it isn't even in all
sides.








We also taught someone trig be encountering trying to find the area in a hexagon with 24cm
perimeter we splitted the shape in to a rectangle and two isosceles triangles having all the sides
having 4 cm lengths. While doing that we figured that we needed to use trig to find the length of
triangle and the rectangle.