Question

$f(x) = 2x^{2} +5x-2$

Answer 1

Answer:

$f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5}$

Step-by-step explanation:

$f(x) = 2 {x}^{2} + 5x - 2$

$f(x) = 2( {x}^{2} + \frac{5}{2} x) - 2$

$f(x) = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2$

$f(x) + 2 \times \frac{25}{16} = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2$

$f(x) = 2(x + \frac{5}{4} {)}^{2} - 2 - \frac{25}{8}$

$f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5}$