Question

Hi :) I don’t understand the inequality part ... anyone able to help? Thank you :)!

Answer 1

Completing the square gives

$x^2+3x-6=x^2+3x+\dfrac94-\dfrac{33}4=\left(x+\dfrac32\right)^2-\dfrac{33}4$

Then

$f(x)=\left(x+\dfrac32\right)^2-\dfrac{33}4\ge0-\dfrac{33}4=-\dfrac{33}4$

and -33/4 = -8.25, so your answer is correct.