Explicație pas cu pas:
1.
[tex]f(x)=ax²+bx+c \\ f(1) = -3 = > a+b+c = - 3 \\ f(-1) = 9 = > a - b+c = 9 \\ f(0) = 1 = > c = 1 \\ a+b = - 4 \\ a - b = 8 \\ 2a = 4 = > a = 2 \\ b = - 4 - 2 = > b = - 6 \\ = > f(x)=2x² - 6x+1[/tex]
2.a)
[tex]f(x)=a {x}^{2} + bx + c [/tex]
[tex]f(x)= a {(x + \frac{b}{2a} )}^{2} + \frac{ - Δ}{4a}[/tex]
[tex]f(x)=x²-6x+11[/tex]
[tex]Δ = {b}^{2} - 4ac = ( - 6)^{2} - 4 \times 1 \times 11 = 36 - 44 = - 8[/tex]
[tex]f(x)= {(x + \frac{ - 6}{2 \times 1}) }^{2} + \frac{ -( - 8) }{4 \times 1} \\ = > f(x)= {(x - 3)}^{2} + 2[/tex]
b)
[tex]f(x)=-3x²+2x+4 [/tex]
[tex]Δ = {b}^{2} - 4ac = 2^{2} - 4 \times( - 3) \times 4 = 4 + 48=52[/tex]
[tex]f(x)=( - 3) {(x + \frac{ 2}{2 \times ( - 3)}) }^{2} + \frac{ -52 }{4 \times ( - 3)} [/tex]
[tex] = > f(x)= - 3 {(x - \frac{1}{3} )}^{2} + \frac{13}{3}[/tex]
