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Sketching a Quadratic Function by Firstly Expressing It in Completed Square Form

The mathematical solution explains how to sketch the function f(x) = x[sup]2[/sup] + 6x + 8 by firstly expressing the function in completed square form. A detailed explanation of how to find the completed square form is given. The graph of y = x[sup]2[/sup] is then drawn followed by a series of transformations to find the coordinates of the minimum point. The explanation continues to explain how to find the values of intersection with the x axis, by solving the equation f(x) = 0 by both factorisation and using the completed square form. The point of intersection with the y axis is then found by substituting x = 0 into f(x).

The graphical solution explains how to use the graphic calculator to draw the graph of y = f(x), how to check the value of the minimum point and how to check where the graph crosses the axes. The video explains how to alter the scale of the graph in order to show all the points of intersection and then how to locate the key points on the graph.

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