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.
x = - 3 , vertex : ( - 3 , - 8 ), Number of real solutions : 2.
a 1 = - 3 ,  a 2 = - 3 , a 3 = - 8 ,  a 4 = 2. 

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