Horizontal Parabola Formula
The formula for a horizontal parabola can be written in the general form:
(x – h)^2 = 4p(y – k)
In this formula, the vertex of the parabola is (h, k), and the value of p determines the location of the focus and the directrix
The formula for a horizontal parabola can be written in the general form:
(x – h)^2 = 4p(y – k)
In this formula, the vertex of the parabola is (h, k), and the value of p determines the location of the focus and the directrix.
Let’s break down the different components of this formula:
1. (x – h)^2: This represents the horizontal shift of the parabola. The value h represents the x-coordinate of the vertex, where the parabola reaches its minimum or maximum point horizontally. The term (x – h)^2 is squared to ensure that the parabola opens either to the left (if the coefficient is positive) or to the right (if the coefficient is negative).
2. y – k: This represents the vertical shift of the parabola. The value k represents the y-coordinate of the vertex, where the parabola reaches its minimum or maximum point vertically. The term (y – k) is not squared because it does not affect the direction of the opening of the parabola.
3. 4p: This determines the steepness of the parabola and the distance between the vertex and the focus/directrix. The value of p is positive if the parabola opens to the right and negative if it opens to the left. The distance from the vertex to the focus and the directrix is given by |p|.
To graph a horizontal parabola, follow these steps:
1. Identify the vertex (h, k) from the equation.
2. Determine the value of p.
3. Use the vertex as the starting point and plot it on the coordinate plane.
4. Based on the value of p, plot the focus and the directrix. The focus is located at a distance of |p| units to the right or left of the vertex, and the directrix is a horizontal line located at a distance of |p| units from the vertex.
5. Draw a smooth curve through the vertex, touching the focus and being equidistant from the directrix.
Understanding and utilizing the horizontal parabola formula will allow you to accurately graph and solve problems related to horizontal parabolas.
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