7.
f(x) = a(x - p)² + q - postać kanoniczna funkcji kwadratowej
f(x) = 3(x + 2)² - 4
W = (p,q)
Ze wzoru funkcji odczytujemy:
p = -2
q = -4
W = (p,q)
W = (-2, -4)
8.
[tex]3x(x+3) < (x+3)^{2}\\\\3x^{2}+9x < x^{2}+6x+9\\\\3x^{2}-x^{2}+9x -6x-9 < 0\\\\\underline{2x^{2}+3x-9 < 0}\\\\a = 2, \ b = 3, \ c = -9\\\\\Delta = b^{2}-4ac = 3^{2}-4\cdot2\cdot(-9) = 9 + 72 = 81\\\\\sqrt{\Delta} = \sqrt{81} = 9\\\\x_1 = \frac{-b-\sqt{\Delta}}{2a} = \frac{-3-9}{2\cdot2} = \frac{-12}{4} = -3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-3+9}{4}=\frac{6}{4} = \frac{3}{2} = 1,5[/tex]
[tex]a > 0, \ to \ parabola \ zwrocona \ jest \ ramionami \ do \ gory,wowczas:\\\\\boxed{x \in (-3; 1,5)}[/tex]
