The-Organic-Chemistry-Tutor
This video teaches viewers how to find the focus and directrix of a parabola, and how to graph parabolic equations. The video covers finding the vertex, using the p value to determine the direction of the parabola, and finding the coordinates of the focus and directrix. The length of the latus rectum is also calculated, and the domain and range of the function are determined. The process of completing the square is demonstrated, and viewers are advised to understand these concepts to graph parabolic equations more easily.
In this section, the instructor goes over the equations needed to find the focus and directrix of a parabola. They explain that the equation y squared equals 4px is used when the vertex of the parabola is at the origin, while the equation x squared equals 4py is used when the vertex is at the origin as well. P is the distance between the vertex and the focus, and the directrix is p units away from the vertex. The instructor also explains that the lattice rectum, which has a length of 4p, connects the focus to the curve. The section ends with an example problem of graphing an equation using the p value.
In this section, the video covers finding the focus and directrix of a parabolic equation and determining the length of the latus rectum. The video explains how to graph a parabolic equation and how to associate the correct orientation of the parabola with the appropriate equation. The viewer is advised to understand this concept to graph parabolic equations more easily, especially for harder versions.
In this section, the video covers finding the focus and directrix of a parabola, as well as writing the standard form of the equation for a parabola with given conditions. The vertex is found by taking the midpoint between the focus and the directrix, with the vertex being at the origin in this example. Additionally, the video covers how to determine the value of p and the direction that the parabola opens, with the equation ultimately being y squared equals negative 12x. The video also goes on to cover finding the coordinates of the vertex and focus, as well as the equation of the directrix and graphing the parabola. The length of the latus rectum and the domain and range of the function are also calculated.
In this section, the video explains how to find the focus and directrix of a parabola by first writing the equation of the parabola in vertex form. The vertex and focus are located using information from this equation and the graph of the parabola, while the directrix formula is used to find the equation of the directrix. The length of the latus rectum is also calculated, and the domain and range are determined. By following these steps, all the important features of the parabola can be found.
In this section, the instructor discusses finding the range and domain of a horizontal and vertical parabola respectively. They then move on to identifying the coordinates of the vertex and focus for a specific parabola and calculate the value of p. Based on the value of p, they demonstrate that the parabola opens downward and find the coordinates of the focus using the formula h, k + p. They then find other necessary points to sketch the parabola. Finally, using the equation of the directrix, they complete the graph.
In this section, the length of the lattice rectum of a parabola is determined, and the domain and range of a vertical parabola are discussed. Additionally, the equation of a parabola in standard form is obtained through completing the square. The coordinates of the vertex and focus are identified, the equation of the directrix is written, and the parabola is graphed. The process of completing the square is demonstrated step by step, with the x and y variables kept on separate sides of the equation. Finally, the equation is simplified and written in standard form with the variables in the correct format.
In this section, the focus and directrix of a vertical parabola are found by first determining the vertex, which has coordinates (2,-1), and using the formula for p, which is equal to 2. From there, the direction of the parabola is determined to be upward and the focus is found to have coordinates (2,1) by using the formula for the focus. The other points on the parabola are then found by traveling 2p to the right and left of the focus, giving a rough approximation of the graph. Finally, the directrix is found by using the formula and is determined to be y = -3. The equations for the focus and directrix are confirmed using their respective formulas.
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