Question 688315
the values of the quadratic equation ({{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}})
1.

{{{F(x)=(1/2)x^2 -4}}}.....plug in {{{x=-2}}}

{{{F(-2)=(1/2)(-2)^2 -4}}}

{{{F(-2)=(1/2)4 -4}}}

{{{F(-2)=(1/cross(2))cross(4)2 -4}}}

{{{F(-2)=2-4}}}

{{{F(-2)=-2}}}


{{{F(x)=(1/2)x^2 -4}}}.....plug in {{{x=-1}}}

{{{F(-1)=(1/2)(-1)^2 -4}}}

{{{F(-1)=(1/2)1 -4}}}

{{{F(-1)=1/2 -4*2/2}}}

{{{F(-1)=(1-8)/2}}}

{{{F(-1)=-7/2}}}

{{{F(-1)=-3.5}}}


{{{F(x)=(1/2)x^2 -4}}}.....plug in {{{x=0}}}

{{{F(0)=(1/2)(0)^2 -4}}}

{{{F(0)=(1/2)0 -4}}}

{{{F(0)=-4}}}


{{{F(x)=(1/2)x^2 -4}}}.....plug in {{{x=1}}}

{{{F(1)=(1/2)(1)^2 -4}}}

{{{F(1)=(1/2)1 -4}}}

{{{F(1)=1/2 -4*2/2}}}

{{{F(1)=(1-8)/2}}}

{{{F(1)=-7/2}}}

{{{F(1)=-3.5}}}


{{{F(x)=(1/2)x^2 -4}}}.....plug in {{{x=2}}}

{{{F(2)=(1/2)(2)^2 -4}}}

{{{F(2)=(1/2)4 -4}}}

{{{F(2)=(1/cross(2))cross(4)2 -4}}}

{{{F(2)=2-4}}}

{{{F(2)=-2}}}

so, you have these points:

({{{-2}}},{{{-2}}})

({{{-1}}},{{{-3.5}}})

({{{0}}},{{{-4}}})

({{{1}}},{{{-3.5}}})

({{{2}}},{{{-2}}})


{{{drawing(600,600,-10,10,-10,10,grid(1),circle(-2,-2,0.2),circle(-1,-3.5,0.2),circle(0,-4,0.2),circle(1,-3.5,0.2),circle(2,-2,0.2),graph(600,600,-10,10,-10,10,(1/2)x^2 -4))}}}


2.

given: ({{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}})

{{{F(x)=(x+4)^2 - 1}}}........plug in {{{x=-2}}}

{{{F(-2)=(-2+4)^2 - 1}}}

{{{F(-2)=(2)^2 - 1}}}

{{{F(-2)=4 - 1}}}

{{{F(-2)=3}}}



{{{F(x)=(x+4)^2 - 1}}}........plug in {{{x=-1}}}

{{{F(-1)=(-1+4)^2 - 1}}}

{{{F(-1)=(3)^2 - 1}}}

{{{F(-1)=9 - 1}}}

{{{F(-1)=8}}}


{{{F(x)=(x+4)^2 - 1}}}........plug in {{{x=0}}}

{{{F(0)=(0+4)^2 - 1}}}

{{{F(0)=(4)^2 - 1}}}

{{{F(0)=16 - 1}}}

{{{F(0)=15}}}


{{{F(x)=(x+4)^2 - 1}}}........plug in {{{x=1}}}

{{{F(1)=(1+4)^2 - 1}}}

{{{F(1)=(5)^2 - 1}}}

{{{F(1)=25 - 1}}}

{{{F(1)=24}}}


{{{F(x)=(x+4)^2 - 1}}}........plug in {{{x=2}}}

{{{F(2)=(2+4)^2 - 1}}}

{{{F(2)=(6)^2 - 1}}}

{{{F(2)=36 - 1}}}

{{{F(2)=35}}}

the points are:

({{{-2}}},{{{3}}})

({{{-1}}},{{{8}}})

({{{0}}},{{{15}}})

({{{1}}},{{{24}}})

({{{2}}},{{{35}}})


{{{drawing(600,600,-10,10,-10,40,grid(1),circle(-2,3,0.2),circle(-1,8.5,0.2),circle(0,15,0.2),circle(1,24.5,0.2),circle(2,35,0.2),graph(600,600,-10,10,-10,40,(x+4)^2 - 1))}}}