Resposta:
Parábola:
Pontos:
(-2,0) ; (0,8); (4,0)
[tex]f(0) = \\ \\ a( {0)}^{2} + b(0) + c = 8 \\ \\ c = 8[/tex]
[tex]f(x) =a {x}^{2} + bx + c \\ \\ f( - 2) = \\ a( - 2)^{2} + b( - 2) + 8 = 0 \\ \\ 4a - 2b + 8 = 0 \\ \\ f(4) = \\a( {4}^{2} ) + b(4) + 8 = 0 \\ \\ 16a + 4b + 8 = 0 \\ \\ (4a - 2b + 8 = 0 ) \times 2\\ 16a + 4b + 16 = 0 \\ \\ 8a - 4b + 16 = 0 \\ 16a + 4b + 8 = 0(somando) \\ \\ 24a + 24 = 0 \\ \\ 24a = - 24 \\ \\ a = \dfrac{ - 24}{24} \\ \\ \blue{a = - 1}[/tex]
Reta:
Pontos:
(0,-1); (1/2,0)
[tex]f(x) = ax + b \\ \\ f(0) = \\ \\ a(0) + b = - 1 \\ \\ b = - 1 \\ \\ f( \dfrac{1}{2} ) = \\ \\ a( \dfrac{1}{2} ) - 1 = 0 \\ \\ \dfrac{a}{2} = 1 \\ \\ \blue{ a = 2}[/tex]
Bons Estudos!
