Question

Determine os valores de a e b para que a função y = ax² + bx + 3 tenha vértice v = (1,4). Por favor, me ajudem

Answer 1

$-\frac{b}{2a} = 1 \\\\ b = -2a \\\\\\ -\frac{b^2 -4ac}{4a} = 4 \qquad \rightarrow C = 3 \\\\ -\frac{b^2 -12a}{4a} = 4 \qquad \rightarrow b = -2a \\\\ -\frac{(-2a)^2 -12a}{4a} = 4 \\\\ -\frac{4a^2 -12a}{4a} = 4 \\\\ -(a - 3) = 4 \\\\ a = -1 \\\\\\ b = -2a \\\\ b = -2 \cdot (-1) \\\\ b = 2$