Respuesta :
[tex]\begin{gathered} \text{ Suppose we know that }g(u)=au^2+bu^{}+c,\text{ and that} \\ g(3)=0,g(-1)=0,\text{ and }g(0)=0.36,\text{ then this is equivalent to saying} \\ (3,0),(-1,0),(0,0.36)\text{ lie on the graph }g \\ \text{ These three points of the following equations} \\ 0=a(3)^2+b(3)+c\rightarrow0=9a+3b+c\text{ }(1) \\ 0=a(-1)^2+b(-1)+c\rightarrow0=a-b+c(2)_{}_{} \\ 0.36=a(0.36)^2+b(0.36)+c\rightarrow0.36=0.1296a+0.36b+c\text{ }(3) \\ \text{ Then subtract eq 1 from eq2 to get equation 4, then eq2 from eq3, and get eq5} \\ 8a+4b=0\text{ }(4) \\ 0.8704a-1.36b=-0.36\text{ }(5) \\ \text{ From equation 4 we get that} \\ 4b=-8a \\ b=-2a \\ \text{Substitute to eq 5} \\ 0.8704a-1.36(-2a)=-0.36 \\ 0.8704a+2.72a=-0.36 \\ 3.5904a=-0.36 \\ a=-\frac{75}{748} \\ \text{ Substitute it to eq1 get b and we get} \\ b=\frac{75}{374} \\ \text{ And since g(0)=0.36, then c=0.36 or} \\ c=\frac{9}{25} \\ g(u)=-\frac{75}{748}x^2+\frac{75}{374}x+\frac{9}{25} \end{gathered}[/tex]
