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find the x-intercepts of the parabola with vertex -1,-108 and y-intercept 0, -105. in the form (x1,y1)(x2,y2).

Sagot :

kate200468
[tex]y=a(x-x_V)^2+y_V\ \ \ and\ \ \ Vertex=(x_V,y_V)=(-1,-108)\\\\y=a(x+1)^2-108\\\\y-intercept:\ (0,-105)\\ \Rightarrow\ \ \ -105=a(0+1)^2-108\ \ \ \Rightarrow\ \ \ a=3\\\\y=3(x+1)^2-108\\y=3[(x+1)^2-36]=3(x+1-6)(x+1+6)=3(x-5)(x+7)\\\\x-intercept:\ y=0\\\Rightarrow\ \ \ 3(x-5)(x+7)=0\\.\ \ \ \ \ \Leftrightarrow\ \ \ x-5=0\ \ \ or\ \ \ x+7=0 \ \ \ \Leftrightarrow\ \ \ x=5\ \ \ or\ \ \ x=-7\\\\Ans.\ (x_1,y_1)=(5,0),\ \ \ (x_2,y_2)=(-7,0)[/tex]
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