Eliminate the parameter to obtain a horizontal parabola

The video tutorial explains how to solve for T in the X equation, highlighting the introduction of square roots and the implications of plus or minus signs. It discusses the properties of parabolas, including their orientation based on equations like Y = X^2 and Y = -X^2. The tutorial guides through solving the equation step-by-step, emphasizing the role of square roots in creating sideways parabolas. It concludes with a practical exercise using a calculator to visualize the concepts.

What is a key consideration when introducing square roots in an equation?

• The equation becomes quadratic.

• You must consider both positive and negative roots.

• You can ignore negative roots.

• The equation becomes linear.

What shape does the equation y = X^2 form?

• A line

• A sideways parabola

• A parabola opening up

• A circle

How does the parabola y = -X^2 differ from y = X^2?

• It opens to the right.

• It opens downwards.

• It forms a circle.

• It opens upwards.

What happens to the parabola when you solve for T in the equation X - 3 = T^2?

• It becomes a vertical line.

• It forms a sideways parabola.

• It becomes a circle.

• It forms a parabola opening upwards.

If y^2 is positive, in which direction does the parabola open?

• Downwards

• Upwards

• To the right

• To the left