QUADRATIC FUNCTIONS Solving Quadratic Inequalities (Page 2 of 2)

We now interpret the inequality x^2-2x-7 >= 0 in terms of the function we have graphed. The solution set will be all values of x for which the function Y1 has positive or zero y-values. Let's use TRACE to identify where these values of x are.

 TRACE key. Left arrow key....

 Right arrow key....

 Calculator screen image. Calculator screen image. Calculator screen image.

Since the x-intercepts have a y-value of 0, they are part of the solution set. The x-values to the left of -1.83 yield positive y-values, as well as the x-values to the right of 3.83. The inequality x^2-2x-7 >= 0 means that the graph of Y1 (the parabola) must lie on or above the x-axis. Looking at the graph, we observe this is true if x is to the left of -1.83 or to the right of 3.83. So, the solution set is approximately {x: x <= -1.83 or x >= 3.83}, or in interval notation, (-infinity, -1.83]U[3.83, infinity).
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