Question

How do you write a quadratic function in standard form whose graph passes through points (-1,-2), (1,-4), (2,1)?

Answer 1

$let \: the \: general \: eq \\ y = ax {}^{2} + bx + c \\ eqn \: pass \: from \: ( - 1 \: .- 2) \\ a - b + c = - 2 \: - - - - (1) \\ eqn \: pass \: from \: ( 1 \: . - 4) \\ a + b + c = - 4 - - - - (2)\\ eqn \: pass \: from \: ( 2 \: .1) \\ 4a + 2b + c = 1 - - - - (3) \\ adding \: 1 \: and\: 2 \\ a + c = - 3 \: \\ b = - 1 \\putting \: in \: (3) \\ 3a + (a + c) + 2b = 1 \\ 3a + - 3 + - 2 = 5 \\ a = \frac{10}{3} \\ c = \frac{ - 19}{3} \\ put \: in \: eq \\ \\ y = \frac{10}{3} {x}^{2} - x + - \frac{19}{3} )$