How to write the standard equation of a parabola given the focus and vertex

The video tutorial explains how to write the equation of a parabola given its vertex and focus. It begins by determining the direction in which the parabola opens by plotting the vertex and focus. The tutorial then derives the equation using the vertex at the origin and calculates the parameter P, which represents the distance from the vertex to the focus. The final equation is presented, and the tutorial concludes with a summary of the process.

What is the first step in determining the direction a parabola opens?

• Solving for the value of P

• Identifying the directrix

• Plotting the given points

• Calculating the distance between the focus and vertex

Which variable is squared in the equation of a parabola that opens to the left?

• H

• Y

• X

• K

What does the variable P represent in the equation of a parabola?

• The distance from the focus to the directrix

• The distance from the vertex to the focus

• The distance from the vertex to the directrix

• The distance from the vertex to the axis of symmetry

How is the value of P determined in this problem?

• By measuring the distance from the vertex to the directrix

• By measuring the distance from the focus to the directrix

• By measuring the distance from the vertex to the axis of symmetry

• By measuring the distance from the vertex to the focus

What is the final form of the equation for the parabola in this problem?

• y^2 = 4px

• x^2 = 4py

• y^2 = -10x

• x^2 = -10y