Question

URGENT!! MAINE NE DA 3 DACA NU AVEM TEMA :( DECI VA ROG FRUMOS, AJUTATI-MA !!!!​

Answer 1

$Fie \:f:\mathbb{R}\rightarrow\mathbb{R}\:\:\:,f(x) = a{x}^{2} + bx + c$

$A(-1,-3)\:\in\:G_{f} = > f( - 1) = - 3$

$a \times {( - 1)}^{2} + b \times ( - 1) + c = - 3$

$a - b + c = - 3$

$B(1,4)\:\in\:G_{f} = > f(1) = 4$

$a \times {1}^{2} + b \times 1 + c = 4$

$a + b + c = 4$

$C(0,2)\:\in\:G_{f} = > f(0) = 2$

$a \times {0}^{2} + b \times 0 + c = 2$

$c = 2$

$a - b + c = - 3$

$a - b + 2 = - 3$

$a - b = - 3 - 2$

$a - b = - 5$

$a + b + c = 4$

$a + b + 2 = 4$

$a + b = 4 - 2$

$a + b = 2$

$\left\{\begin{matrix} a - b = - 5\\ a + b = 2 \end{matrix}\right.$

$2a = - 3$

$a = - \frac{3}{2}$

$a + b = 2$

$- \frac{3}{2} + b = 2 \: | \times 2$

$- 3 + 2b = 4$

$2b = 4 + 3$

$2b = 7$

$b = \frac{7}{2}$

$= > f(x) = - \frac{3}{2} {x}^{2} + \frac{7}{2} x + 2$