F ( x ) = ( x + 3 )² - 8 = x² + 6 x + 9 - 8 = x² + 6 x + 1 For the quadratic function: Axis of symmetry is: x = -b/ 2 a, where: a = 1, b = 6 ( because it it in the form: y = a x² + b x + c ). Therefore: x = -6 / 2 = -3. f ( - 3 ) = ( - 3 + 3 )² - 8 = 0 - 8 = - 8 And D = b² - 4 a c = 6² - 4 * 1 * 1 = 36 - 4 = 32 ( greater than 0 ). It means that there are 2 real solutions. Answer: x = - 3 , vertex : ( - 3 , - 8 ), Number of real solutions : 2. a 1 = - 3 , a 2 = - 3 , a 3 = - 8 , a 4 = 2.
