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A. Introducing Quadratic Functions

Just as all graphs of all linear functions are straight lines, the graphs of all quadratic functions are parabolas. In the same way that linear functions are unique, depending on the slope and the \(y\)-intercept, quadratic functions are unique depending on the location of the vertex and the value of the variable , \(a \), in the equation \(f(x) = a(x - p)^2 + q \). In the Investigation above, you examined characteristics of the most basic quadratic function, \(y = x^2 \). In Example 1, you explore the change in characteristics for the graph of a more complex quadratic function.