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電子課本網(wǎng) 第26頁

第26頁

信息發(fā)布者:
解:???$(1)$???拋物線的頂點坐標為???$(5,$??????$5),$???
與???$y$???軸交點坐標是???$(0,$??????$1),$???
設(shè)拋物線的解析式是???$y=a(x-5)^2+5,$???
把???$(0,$??????$1)$???代入???$y=a(x-5)^2+5,$???
得???$a=-\frac {4}{25},$???
???$∴y=-\frac {4}{25}(x-5)^2+5(0≤x≤10).$???
???$(2)$???由已知得兩景觀燈的縱坐標都是???$4,$???
???$∴4=-\frac {4}{25}(x-5)^2+5,$???
???$∴\frac {4}{25}(x-5)^2=1,$???
???$∴x_1=\frac {15}{2},$??????$x_2=\frac {5}{2},$???
∴兩景觀燈間的距離為???$\frac {15}{2}-\frac {5}{2}=5($???米).
解:??$(1)$??以??$O$??為原點,頂點為??$(1,$????$2.25),$??
設(shè)解析式為??$y=a(x-1)^2+2.25$??過點??$(0,$????$1.25),$??
解得??$a=-1,$??
所以解析式為:??$y=-(x-1)^2+2.25,$??
令??$y=0,$??
則??$-(x-1)^2+2.25=0,$??
解得??$x=2.5 $??或??$x=-0.5($??舍去),
所以花壇半徑至少為??$2.5m.$??
??$(2)$??根據(jù)題意得出:
設(shè)??$y=-x^2+bx+c,$??
把點??$(0,$????$1.25),$????$(3.5,$????$0)$??代入,可得
??$∴\{ \begin{array}{l}{c=1.25}\\{-\frac {49}{4}+\frac {7}{2}b+c=0} \end{array} ,$??
解得:
??$\{ \begin{array}{l}{b=\frac {22}{7}}\\{c=\frac {5}{4}} \end{array} .$??
??$∴y=-{x}^2+\frac {22}{7}\frac {5}{4}=-{(x-\frac {11}{7})}^2+\frac {729}{196},$??
∴水池的半徑為??$3.5m,$??要使水流不落到池外,此時水流最大高度應(yīng)達??$\frac {729}{196}$??米.
???$∵\frac {729}{196}≈3.7$???
∴最大高度為???$3.7$???米