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In this video, we learn how to find the equation of a parabola with a vertex located outside of the origin. First, we recall that the parabola always opens to the right due to the fact that the focal point is always located to the right of the vertex. Next, we sketch out the parabola using a horizontal coordinate system. We then need to use a formula we learned earlier to find the coordinates of the vertex, which are (h, k). The vertex is located at (h, k), which means that h = k and that a = c-h. We then need to substitute these values into the equation of the parabola, which results in the following equation: a horizontal equation with the following structure: -(x-h)^2 = 4(a-k) - (y-k)^2. This is the equation we will use to find the distance between the vertex and the focus. Finally, we return to our original sketch and find all of the points that satisfy our equation.

**00:00:00**In this video, Jesus Grajeda explains the formulas for vertical and horizontal parabolae, and demonstrates an example. He also explains a practice for solving eigenvalue problems, and gives a brief explanation of a parabola's vertex and focus. Finally, he shows how to solve a parabola with a vertex located outside the origin using two equations.**00:05:00**In this video, we learn how to find the equation of a parabola with a vertex outside of the origin. First, we recall that the parabola always opens to the right due to earlier videos in which we saw that the parabola always surrounds the focal point. Next, we sketch out the parabola using a horizontal coordinate system. We then need to use a formula we learned earlier to find the coordinates of the vertex, which are (23, 2). The vertex is located at (23, 2), which means that h = 2 and that ac-here (23, 3). We then need to substitute these values into the equation of the parabola, which results in the following equation: a horizontal equation with the following structure: - here, the square is equal to 4 minus px, and this is the equation we will use - x is equal to 4 minus 3x, which is 3, and p is equal to 3. Next, we find the distance from the vertex to the focal point by substituting these values into the distance formula: 1-2 + 3 = 4. This results in a distance of 3 units from the vertex to the focal point. Finally, we return to our original sketch and find all**00:10:00**In this video, the author explains how to find the distance between a vertex and the focus of a parabola. The distance between the vertex and the focus is the same as the distance between the vertex and the directrix, which is 3. The author then shows how to calculate the equation of the directrix and the equation of the axis.

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