Focus and Directrix of a Parabola 2  Summary and Q&A
TL;DR
The video explains how to find the focus and directrix of a parabola given its equation in the form y  y1 = A(x  x1)^2.
Questions & Answers
Q: How can the equation y  y1 = A(x  x1)^2 be used to find the focus and directrix of a parabola?
By pattern matching, the xcoordinate of the focus is equal to the xcoordinate of the vertex, while the ycoordinate of the focus is determined by adding 1/(4A) to the ycoordinate of the vertex. The directrix is located 1/(4A) below the ycoordinate of the vertex.
Q: What is the importance of the vertex in finding the focus and directrix?
The vertex serves as a key point in determining the position of the focus and directrix. Its xcoordinate is the same as the xcoordinate of the focus, while its ycoordinate is used to calculate the ycoordinate of the directrix.
Q: How can the equation y  y1 = A(x  x1)^2 be graphed to visualize the focus and directrix?
The vertex, located at the point (x1, y1), represents the lowest or highest point on the parabola. The focus is located 1/(4A) units above the vertex, while the directrix is located 1/(4A) units below the vertex. The graph of the parabola will be symmetric with respect to the line of the directrix.
Q: What is the significance of the scaling factor, A, in the parabola equation?
The scaling factor, A, determines the steepness of the parabola. A larger value of A makes the parabola narrower, while a smaller value makes it wider. The reciprocal of 4A is used to calculate the distance between the vertex and the focus/directrix.
Summary & Key Takeaways

The video demonstrates how the equation y  y1 = A(x  x1)^2 can be used to find the focus and directrix of a parabola.

By pattern matching, the xcoordinate of the focus is equal to the xcoordinate of the vertex.

The ycoordinate of the focus is determined by adding 1/(4A) to the ycoordinate of the vertex.

The directrix is located 1/(4A) below the ycoordinate of the vertex.