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The video demonstrates two methods for determining the equation of a quadratic function from its graph. The first method involves finding the vertex point and one other point on the graph, using the vertex form of the quadratic formula. The second method requires finding the y-intercept and two other points, allowing for the use of the elimination method to solve for A, B, and C in standard form. These methods make it possible to find the quadratic function that corresponds to any given graph.
In this section, the video explains how to find the equation of a quadratic function from a graph, given the vertex point and another point on the graph. Using the vertex form of a quadratic formula, which is y equals a times x minus H squared plus K, the video explains that if you know the vertex, you only need one more point. The standard form of the equation requires three points to find the quadratic function. The video presents two examples, one with two given points and the vertex, and another with three given points, where the vertex is not known and the standard form is used.
In this section, a method for finding the equation of a quadratic function from three points on its graph is discussed. The process begins by finding the y-intercept, which can be used to determine the value of C. The x-intercept can also be found by replacing Y with 0 and solving for X. This information helps to determine the values of A and B, which can be used to solve for the equation. By using the elimination method, users can solve for A and B, and subsequently, C. The final quadratic equation can then be written in standard form using the values of A, B, and C found.
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