The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. The function is quadratic,RAINFALL(in.) .POPULATION (millions.) 0. . 0 1. . 9 3. . 21 4. .24 5. . 25 6. . 24The x-intercept represents that after _____ in. of rain there are mosquities.( I cant seem to wrap my head around this, If you can just help me start somehwere i'd really appriciate it. Also I noticed the pattern in mosquitoes.)
Accepted Solution
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Answer:The x-intercept represents that after 10 in. of rain there are mosquitoes.Step-by-step explanation:The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. The function is quadratic, [tex]P(x)=ax^2+bx+c[/tex]where, P represents number of mosquitoes in millions. x represents rainfall in inches. Table : x : 0 1 3 4 5 6 P : 0 9 21 24 25 24Using three point to make system of equation and solve for coefficients a, b and c Put (0,0) and we get [tex]c=0[/tex]Put (1,9) and we get [tex]a+b+c=9[/tex]Put (3,21) and we get [tex]9a+3b+c=21[/tex]Solve for a, b and c [tex]a=-1[/tex][tex]b=10[/tex][tex]c=0[/tex][tex]P(x)=-x^2+10x[/tex]Now, we will find x-intercept of the function. Put P(x)=0 and solve for x [tex]-x^2+10x=0[/tex][tex]x=0,10[/tex]The x-intercepts represent number of mosquitoes after 10 in of rain fall.