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Mathematics Senior High

-a^2+2a=-(a-1)^2+1とあるのですが、これの右の項はどこから出てきて、この式は何を表しているのですか?

aは正の定数とし,2次関数f(x)=x°-2ax+2a (0ハx^2)の最小値を, 場合分けされたaの値の範囲で求めた m(a) に対し, b=m(a) のグラフを考えることで、 OO000 指針>関数のグラフ (下に凸の放物線)の軸は直線x=aであるが, aのとる値によって軸の位量 134 基本 例題81 最大値, 最小値を関数ととらえる問題 : mla)と する。このとき,m(a) の最大値とそのときのaの値を求めよ。 【富山県大) 墓本79 X=a が変わる。最小値を考えるから,軸x=aと区間0ミxミ2の位置関係を調べる 本間では, a>0 であるから, 軸が区間の 内,右外 の場合に分けて考える ac0のをきは 調べなとと良い m(a)の最大値を求める。 解答 (まず,基本形に直す。 関数の式を変形すると f(x)=(x-a)°-a+2a ソ=f(x)のグラフは下に凸の放物線で,軸は直線x=a [1] 0<aS2のとき 小景 図[1] から, x=aで最小となる。 f(a)=-α°+2a (軸が区間の内 a>0であるから,軸が区 間の左外は調べなくてよい。 最小値は [2] a>2のとき 図 [2] から, x=2 で最小となる。 (軸が区間の右外 さ 最小値は f(2)=-2a+4 +%3D |軸 最小 最小 x=0 x=a x=2 x=0 x=2 x=a -a+2a (0<a<2) [1], [2] から m(a)= -2a+4(a>2) -a+2a=-(a-1)+1 ここで ゆえに,b=m(a)とすると, そのグ ラフは右の図の実線部分のようにな 46 40<aS2において, 6=m(a)のグラフは上 凸の放物線で,軸は直線 a=1, 頂点は点(1, 1) ある る。 したがって, m(a) は a=1 で最大 小景 小郡 1 0 2 値1をとる。 1 AS

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English Senior High

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Grammar Focus noun refers to something that cannot be counted (a mass), and so it does not use a plural form. When a noun is countable and it refers to only one person, place or thing, the singular form is used. If the noun refers to more than one, we use the plural form. Plurals are usually created by adding -s to a noun's When a noun is used, it is important to determine if it is countable or uncountable. If uncountable, the singular form, but the spelling of plurals varies and can be irregular. Nouns-Countable / Uncountable Complete each of the following sentences with an appropriate word or phrase. 1. Donating blood is a good way to savea life because patients often require ( to help treat a fatal disease. ) or platelets b. was blood a. a blood C. blood d. its 。Radiation, matter, gravitation, electric charge, and magnetism are all invisible physical a. a phenomenon b. phenomenon C. the phenomenons d. phenomena 3. If people have ( )lasting a week or longer, it may be caused by the flu. a. fever b.a fever C. fevers d. the fevers 4. The ( )are using the forensic science lab report to help them in the investigation. a. detective b. police officer C. polices d. police ) travels in straight lines, and transmits energy from one place to another. a. Light b. The lights C. A light d. Lights ) people think that smoking is healthy, some people do think that smoking is ) people never try to quit smoking. C. few, quite a few 6. Although ( arelaxing tool. Surprisingly, ( a. quite a little, little b. little, quitea few d. quite a few, little ) in the summer camp are interested in nature. a. Most of childs b. The most child c. Most of children d. Most of the children ) can be dangerous if you don't recognize an adverse reaction. b. a medicine 8. Taking a. medicine d. one medicine c. medicines lectronic data exchange via e-mail or the Web is more eco-friendly than using millions of d. sheets of papers a. a sheet of paper c. sheets of paper b. a sheet of papers 10. 7Of the employees in the company are contract workers. c. Number d. Majority a. Lot b. Half

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