8.1 Practice

Front

What does the variable 'y' represent in projectile motion?

Back

The vertical distance a projectile travels.

Front

Given the parametric equations x = 1 - 2t and y = 4t + 1, find the point when t = 3.

Back

(-5, 13)

Front

How do you eliminate the parameter from the equations x = \frac{1}{t-2} and y = 4t - 5?

Back

y = \frac{4}{x} + 3

Front

Sketch the curve represented by the parametric equations x(t) = 2t + 1 and y(t) = t^2 + 2. Which option represents the correct sketch?

Back

Option C

Front

Convert the parametric equations x = 2t and y = t^2 + 3 into rectangular form.

Back

y = \frac{1}{4}x^2 + 3

Front

What is a parametric equation?

Back

An equation that expresses the coordinates of the points of a curve as functions of a variable, usually denoted as 't'.

Front

What is the significance of the variable 't' in parametric equations?

Back

It represents the parameter that defines the position on the curve.

Front

How do you find the x-coordinate from a parametric equation?

Back

Substitute the value of 't' into the equation for x.

Front

What is the relationship between x and y in parametric equations?

Back

They are defined as functions of the same parameter 't', allowing for the representation of curves.

Front

What does the term 'rectangular form' refer to in the context of parametric equations?

Back

It refers to expressing the equations in the form y = f(x) without the parameter.