# Mathematics I (Math 1132)

Durham College, Mathematics
Free
• 42 lessons
• 0 quizzes
• 10 week duration
• ##### Measurements

An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.

• ##### Fractions, Percentage, Ratios and Proportion

Emphasis here is placed on understanding fractions, percent, and using ratios to compare quantities and set up proportions to solve problems.

• ##### Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

## Mathematics I (Math 1132)

### Parametric Equations

Sometimes the input variable, x, and the output variable, y, of an equation might be influenced by a separate factor, t. In other words, the variable, t, influences both the x and the y separately. Such a scenario can be modeled using a parametric. For example, finding the solution to x = t + 1 and y = t ÷ 2 at t = 4 gives the ordered pair:

 $x\left(t\right)=t+4\phantom{\rule{0ex}{0ex}}x\left(4\right)=4+4\phantom{\rule{0ex}{0ex}}x\left(4\right)=8\phantom{\rule{0ex}{0ex}}$ $y\left(t\right)=t}{2}\phantom{\rule{0ex}{0ex}}y\left(4\right)=4}{2}\phantom{\rule{0ex}{0ex}}y\left(4\right)=2\phantom{\rule{0ex}{0ex}}$

∴   Ordered pair: (8, 2)

Notice how the ordered pairs generated from the parametric equations form a parabola. If you’d like to find out the equation to the curve without creating a table of values, you can isolate t from one equation and substitute it into the other equation. The equations again were:

1.   x = 2t
2.   y = t² – 2

The easier of the two equations to isolate for t is (1) because all you need to do is divide both sides of 2:

$\frac{t}{2}=\frac{\overline{)2}x}{\overline{)2}}\phantom{\rule{0ex}{0ex}}t=\frac{x}{2}\phantom{\rule{0ex}{0ex}}$

This gets substituted into (2):

The equation in terms of x-y is called a Cartesian equation, and will produce the exact same parabola as the one in the video.