Question

Coloque a função dada por f(x) = 1 + (x − 1/2) (4x + 1) na forma f(x) = ax2 + bx + c e de os valores de a, b e c.

Answer 1

Utilizando a propriedade distributiva, temos:

$f(x) = 1 + \left( x - \dfrac{1}{2} \right) (4x + 1) \\\\\\f(x) = 1 + 4x^2 + x - \dfrac{1}{2} \cdot 4x - \dfrac{1}{2} \\\\\\f(x) = 1 + 4x^2 + x - 2x - \dfrac{1}{2} \\\\\\f(x) = 4x^2 - 2x + x + 1 - \dfrac{1}{2} \\\\\\\bold{f(x) = 4x^2 - x + \dfrac{1}{2}}$

Portanto, a = 4, b = -1 e c = 1/2.