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Question 2The vertex form of the equation of a horizontal parabola is given by , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebra to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below.Part AMark the focus of the parabola you are going to create at F(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the directrix of your parabola. What is the equation of the line?Font SizesCharacters used: 0 / 15000Part BConstruct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?Font SizesCharacters used: 0 / 15000Part CExplain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.Font SizesCharacters used: 0 / 15000Part DWhich way will the parabola open? Explain.Font SizesCharacters used: 0 / 15000Part EHow can you find the value of p? Is the value of p for your parabola positive or negative? Explain.Font SizesCharacters used: 0 / 15000Part FWhat is the value of p for your parabola?Font SizesCharacters used: 0 / 15000Part GBased on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.Font SizesCharacters used: 0 / 15000Part HConstruct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.Font SizesCharacters used: 0 / 15000Part IOnce you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.Font SizesCharacters used: 0 / 15000Part JTo practice writing the equations of horizontal parabolas, write the equations of these two parabolas in vertex form:focus at (4, 3), and directrix x = 2focus at (2, -1), and directrix x = 8

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Solution:

A typical example of th sparaboa nis shown in the picture below

Part A:

View image AttilaT673827