!"!" +! +!!" +!!"!! +!" +!" +!!"!! +!" +!" +!!"!! +!!" +! like terms Simplified form
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1 . QUADRATIC FUNCTINS. READY, SET,! Name Perid Date READY Tpic: Multiplying tw binmials In the previus RSG, yu were asked t use the distributive prperty n tw different terms in the same prblem. Example:!"#$%&#'!"#!"#$%"&'!! + +! +. Yu may have nticed that the binmial! + ccurred twice in the prblem. Here is a simpler way t write the same prblem:! +! +. Yu will use the distributive prperty twice. First multiply!! + ; then multiply +! +. Add the like terms. Write the x term first, the x-term secnd, and the cnstant term last.!"!" +! +!!" +!!"!! +!" +!" +!!"!! +!" +!" +!!"!! +!!" +! like terms Simplified frm Multiply the tw binmials. (Yur answer shuld have terms and be in this frm!!! +!" +!.).!+! 7.! + 8! +.! 9!.!+!.!! 6.! 7! + 7.! 8! + 8.! + 6! !! SET warm UP Tpic: Distinguishing between linear and quadratic patterns Use first and secnd differences t identify the pattern in the tables as linear, quadratic, r neither. Write the recursive equatin fr the patterns that are linear r quadratic I the the HE ExpTt. 8 7 ft's Quadratic rgy Licensed under the Creative Cmmns Attributin CC BY. Page 7 atx. - s its linear Y If
2 QUADRATIC FUNCTINS I.. x y x y x y t 6 th 68 s H tutt ts 68 sixth tf H S Figure Linear Quadratic Quadratic Figure Figure Figure y 8 f X y Xtxt Figure a. Draw figure. b. Predict the number f squares in figure. Shw what yu did t get yur predictin. Tpic: Interpreting recursive equatins t write a sequence Write the first five terms f the sequence. 7.! = ;!! =!! ! = ;!! =!! 9.! = ;!! =!!.! = 6;!! =!! Licensed under the Creative Cmmns Attributin CC BY. Page
3 QUADRATIC FUNCTINS.. Tpic: Cmparing linear and expnential rates f change Indicate which functin is changing faster.... f(x) g(x) Slpe h(x) m(x) d d(x) w(x)... s(x) r(x) f(x) g(x) p(x) q(x) 6 a. Examine the graph at the left frm t. Whi Which graph d yu think is grwing faster? Hs(x) six r(x) b. Nw b. Nw lk at the graph frm t. Which graph is grwing faster in this interval? rex Licensed under the Creative Cmmns Attributin CC BY. Page
4 QUADRATIC FUNCTINS.. The Trtise and The Hare A Slidify Understanding Task CC BY Paul Dunleavy In the children s stry f the trtise and the hare, the hare mcks the trtise fr being slw. The trtise replies, Slw and steady wins the race. The hare says, We ll just see abut that, and challenges the trtise t a race. The distance frm the starting line f the hare is given by the functin:! =!! (d in meters and t in secnds) Because the hare is s cnfident that he can beat the trtise, he gives the trtise a meter head start. The distance frm the starting line f the trtise including the head start is given by the functin:! =! (d in meters and t in secnds). At what time des the hare catch up t the trtise? y x y x At secnds. If the racecurse is very lng, wh wins: the trtise r the hare? Why?. At what time(s) are they tied? IfIt and secnds. If the racecurse were meters lng wh wins, the trtise r the hare? Why? Rabbit Licensed under the Creative Cmmns Attributin CC BY. Page
5 QUADRATIC FUNCTINS.. Tpic: Identifying dmain and range frm a graph State the dmain and range f each graph. Use interval ntatin where apprpriate. X Et D a. Dmain y Et 9 a. Dmain p f th E l d a. Dmain 6a. Dmain 7a. Dmain 8a. Dmain 9a. Dmain 8 a. Dmain Are the dmains f #9 and # the same? Explain. Licensed under the Creative Cmmns Attributin CC BY. Page 6
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