6.1 Explore Non-Linear Relations
Definitions:
Parabola – a symmetrical U-shaped graph, which is the graph of a quadratic relation.
Quadratic Relation – an equation that describes a parabola, which is of the form y = ax2 + bx + c, where a ≠ 0.
Ex 1:
Construct a table of values between x = -1 and x = 5 for the relation y = x2 – 3 then draw a smooth curve that
joins the points.
x
-1
0
1
2
3
4
5
y
The shape of this specific curve is called a parabola. There are several different types of curves, but in grade 10 math, we
only need to know whether the relation is linear or non-linear and whether the curve is quadratic or not. We also need
to concern ourselves with whether to draw a line or curve of best fit.
Ex 2:
a.)
Draw a line or curve of best fit for each of the following.
b.)
c.)
Ex 3:
a.)
b.)
d.)
Draw the data in each table. Draw a line or curve or best fit through the points. Explain your choice.
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Ex 4:
The formula for the area of a triangle is A = 2 , where b represents the length of the base and h represents the
height. In a right isosceles triangle, the length of the base equals the height.
a.)
Find the area of the right isosceles triangle with each base length from 1cm to 6cm. Record the base lengths
and areas in a table.
Graph the data. Draw a smooth curve through the points.
b.)
a.)
Base Length
(cm)
1
2
3
4
5
6
Area
(cm2)
b.)