How do you write f(x) = x^2 - 5x + 6 in interval notation

Question

f(x) = x²  -  5x - 6 in interval notation

Answer 1

f(x) = x² - 5x + 6 = (x - 2)(x - 3) ; for x < 2    f(x) > 0 ;           ]-inf,2[

                                                    for x = 2    f(x) = 0 ;

                                                    for 2 < x < 3   f(x) < 0 ;     ]2,3[

                                                    for x = 3    f(x) = 0 ;

                                                    for x > 3    f(x) > 0            ]3,+inf[

 

 

f(x) = x² - 5x - 6 = (x + 1)(x - 6) ; for x < -1  f(x) > 0 ;            ]-inf,-1[

                                                   for x = -1   f(x) = 0 ;

                                                   for -1< x < 6  f(x) < 0 ;       ]-1,6[

                                                   for x = 6    f(x) = 0 ;

                                                   f0r x > 6    f(x) > 0              ]6,+inf[

 

I hope it helps you, Sandra. I factorized f(x) using the Sum and Product of roots x₁ and x₂ for a quadratic function 

f(x) = ax² + bx + c with a = 1 ------> f(x) = x² + Sx + P = (x + x₁)(x + x₂)   S = x₁ + x₂    P = x₁ x₂