Given the equation f (x) = (x 3) 2 - 8, fill in the blanks:axis of symmetry: x = a1vertex: (a2, a3) number of real solutions: a4

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.