Quadratics Everything I could want to know Intervals

Quadratics Everything I could want to know.

Intervals of increasing and decreasing. • Consider the following parabola. • The equation is _____ If we go from left to right the quadratic decreases until we get to the vertex. So the interval of decreasing is _____ NOTE WE ALWAYS REPORT THE X. We want to know what x’s will make the function decrease in f(x). (height) Therefore the interval of increasing is ______

If the parabola opens down. • How about this parabola. • • The equation is ________ The interval of decreasing is ______ The interval of increasing is ______ REMEMBER REPORT THE X’S

End Behavior • End Behavior is just where is the height of the function (quadratic) going as x gets very large or very small. • Consider As x gets really big what is f(x) (remember height) of function doing? As x gets really small

More End Behavior • Consider End behavior is almost always written like this In fact with parabolas if they open up f(x) will always approach _____. If they open down f(x) will always approach _____. (now you can impress your friends…. . end behavior and intervals of increasing and decreasing are common Calculus topics)

Example. Lets do it all. • Consider: 1) Find vertex _____ 2) Find AOS: ____ 3) Max or min of ______ 4) Find Y-int: _____ 5) Domain: ____ 6) Range____ 7) Intervals of increasing ____ 8) Intervals of decreasing ____ 9) End Behavior 10) Transformations

Average rate of change (AROC) • Since we cannot find slope of a parabola (yet…. . foreshadowing, calculus) we actually cheat, we can find the average slope between two points. • So for the parabola Find the average rate of change from x=-2 to x=1 Find the ordered pairs (-2, ) and (1, ) and then just find the slope between these points.

AROC continued (-2, 61) and (1, 46) AROC=