We can sketch a parabola using its relationship to the "parent," or most basic parabola, y = x^2. If we know some key points and features of the parent, as well as how changes in the equation affect the graph, we can use words or a sketch to graph a transformed parabola. A change inside the squared base represents a change on x, and will result in a horizontal shift, a change outside the squared base will represent a vertical shift, a negative leading coefficient will reflect the graph across the x axis, and a leading coefficient other than one will cause a vertical stretch or compression. While making a table of values will always work for graphing a parabola, transformations are a very useful shortcut that can be applied to other functions, as well.
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