Answer:
f(x) = 8 (x + ¼)² − ½
Step-by-step explanation:
f(x) = 8x² + 4x
Divide both sides by 8.
1/8 f(x) = x² + 1/2 x
Take half of the second coefficient, square it, then add to both sides.
(½ / 2)² = (1/4)² = 1/16
1/8 f(x) + 1/16 = x² + 1/2 x + 1/6
Factor the perfect square.
1/8 f(x) + 1/16 = (x + 1/4)²
Multiply both sides by 8.
f(x) + 1/2 = 8 (x + 1/4)²
Subtract 1/2 from both sides.
f(x) = 8 (x + 1/4)² − 1/2
