Everything I could want to know. 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: Find vertex _________ 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=