Exploring Parametric Equations and Their Applications

What type of equations are used when X and Y coordinates are calculated separately?

• Parametric equations

• Polar equations

• Linear equations

• Cartesian equations

In projectile motion, how is the horizontal velocity of the object described?

• Decreasing

• Zero

• Increasing

• Constant

What force continuously affects the vertical velocity of a projectile?

• Friction

• Magnetism

• Air resistance

• Gravity

Why might one choose to use parametric equations in modeling?

• To simplify algebraic complexity

• To improve graphical representation

• To handle independent variables

• To reduce calculation time

What is the general form of parametric equations?

• X = F(T), Y = G(T)

• X = G(T), Y = F(T)

• X = T, Y = T^2

• X = T^2, Y = T

What shape is formed when plotting the points from the equations X = 2T and Y = T^2?

• Circle

• Hyperbola

• Parabola

• Ellipse

Which method involves solving for T in one equation and substituting it into another?

• Function integration

• Equation balancing

• Parameter substitution

• Variable elimination

How can you derive a single equation from parametric equations X = 2T and Y = T^2?

• Y = 4X^2

• Y = X/4

• Y = X^2/4

• Y = X^2

What is the result of plugging X/2 into Y = T^2?

• Y = X^2/4

• Y = X/4

• Y = 4X^2

• Y = X^2

What advantage does using parametric equations offer over Cartesian forms in graphing calculators?

• Faster computation

• Easier entry of complex shapes

• More accurate graphs

• Simpler calculations