Summarize the following:
A quadratic inequality takes the form of ax2+bx+c{\displaystyle ax^{2}+bx+c}. Sometimes there may not be an x{\displaystyle x} term or a constant, but there should always be an x2{\displaystyle x^{2}} term on one side of the inequality, and an isolated y{\displaystyle y} variable on the other side. For example, you might need to graph the inequality y<x210x+16{\displaystyle y<x^{2}-10x+16}. To do this, turn the inequality into an equation, and graph the line as you normally would. Since you have a quadratic equation, the line will be a parabola. For example, for the inequality y<x210x+16{\displaystyle y<x^{2}-10x+16}, you would graph the line y=x210x+16{\displaystyle y=x^{2}-10x+16}. The vertex is at point (5,9){\displaystyle (5,-9)}, and the parabola crosses the x-axis at the points (2,0){\displaystyle (2,0)} and (8,0){\displaystyle (8,0)}. Draw the parabola with a dashed line if the inequality is less than (<{\displaystyle <}) or greater than (>{\displaystyle >}). If the value is less than or equal to ({\displaystyle \leq }), or greater than or equal to ({\displaystyle \geq }), you should draw the parabola with a solid line, since the solution includes values equal to the line. For example, for the inequality y<x210x+16{\displaystyle y<x^{2}-10x+16}, you would draw the parabola with a dashed line. In order to determine which area to shade, you need to pick points from inside the parabola, and from outside the parabola. For example, the graph of the inequality y<x210x+16{\displaystyle y<x^{2}-10x+16} shows that the point (0,0){\displaystyle (0,0)} is outside the parabola. This would be a good point to use to test the solution. To determine which area to shade, plug the values of x{\displaystyle x} and y{\displaystyle y} from your test points into the original inequality. Whichever point produces a true inequality indicates which area of the graph should be shaded in. For example, plugging the values of x{\displaystyle x} and y{\displaystyle y} of the point (0,0){\displaystyle (0,0)} into the original inequality, you get:y<x210x+16{\displaystyle y<x^{2}-10x+16}0<020x+16{\displaystyle 0<0^{2}-0x+16}0<16{\displaystyle 0<16}Since this is true, you would shade the area of the graph where the point (0,0){\displaystyle (0,0)} is found. In this case, this is outside of the parabola, not inside of it.

summary: Determine whether you have a quadratic inequality. Graph the line on a coordinate plane. Draw the parabola. Find some test points. Shade the appropriate area.

Summarize the following:
Also: anche So: cosi Perhaps: forse Certainly: certamente Only: solamente At once: subito Also: pure Indeed: davvero Rather: piuttoso Again: di nuovo Yet (still): ancora Just: appena
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