Write the equation of a parabola given vertex, axis of symmetry & point it passes through

The video tutorial explains how to write the equation of an ellipse given the vertex, a point, and the axis of symmetry. It starts by identifying the type of equation based on whether the axis of symmetry is vertical or horizontal. The instructor then plots the vertex and a given point to understand the graph's orientation. Using the vertex form, the equation is formulated, and the focus is calculated by solving for P using the given points. Finally, the equation is finalized, demonstrating how to solve for Y and derive the final equation.

What is the first step in writing the equation of an ellipse when given the vertex, a point, and the axis of symmetry?

• Solve for the variable P.

• Plot the given point on a graph.

• Calculate the distance between the vertex and the focus.

• Determine the type of equation based on the axis of symmetry.

If the axis of symmetry is X = 0, what type of line does it produce?

• A horizontal line

• A curved line

• A diagonal line

• A vertical line

What is the significance of the vertex in the equation of a parabola?

• It is used to find the axis of symmetry.

• It provides the values for H and K in the equation.

• It determines the width of the parabola.

• It helps in identifying the direction of the parabola.

How do you find the value of P in the equation of a parabola?

• By measuring the distance between the vertex and the axis of symmetry.

• By using the formula P = 2/3 X squared.

• By calculating the midpoint of the vertex and the focus.

• By substituting the given point into the equation and solving for P.

What is the final equation of the parabola after calculating P?

• y = 1/2 X squared

• y = 4/3 X squared

• y = 3/2 X squared

• y = 2/3 X squared