Răspuns:
f(x) = x² - 6x + 8
Explicație pas cu pas:
f(0) = 8 => c = 8
[tex]V (3, -1) \iff V \Big(- \frac{b}{2a} ; - \frac{\Delta}{4a} \Big)[/tex]
[tex]- \frac{b}{2a} = 3 \iff b = - 6a[/tex]
[tex]- \frac{\Delta}{4a} = - 1 \iff \Delta = 4a \\ {b}^{2} - 4ac = 4a \iff 36 {a}^{2} - 32a - 4a = 0 \\ 36 {a}^{2} - 36a = 0 \iff36a(a - 1) = 0[/tex]
[tex]a \not= 0 \iff a - 1 = 0 \implies a = 1 \\ \implies b = - 6[/tex]
[tex]\implies \bf f(x) = {x}^{2} - 6x + 8[/tex]
