Obliczam miejsca zerowe
[tex]f(x)=-2x^2+9x+5\\\\a=-2, \ b=9, \ c=5\\\\\Delta=b^2-4ac\Rightarrow9^2-4\cdot(-2)\cdot5=81+40=121\\\\\sqrt{\Delta}=\sqrt{121}=11\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-9-11}{2\cdot(-2)}=\frac{-20}{-4}=\boxed5\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-9+11}{2\cdot(-2)}=\frac{2}{-4}=\boxed{-0,5}[/tex]
Obliczam wierzchołek
[tex]f(x)=-2x^2+9x+5\\\\\text{W}=(p,q)\Rightarrow p=\frac{-b}{2a} \ \text{oraz} \ q=\frac{-\Delta}{4a}\\\\p=\frac{-9}{2\cdot(-2)}=\frac{-9}{-4}=\frac{9}{4}\\\\q=\frac{-121}{4\cdot(-2)}=\frac{-121}{-8}=\frac{121}{8}\\\\\huge\boxed{\text{W}=(\frac{9}{4};\frac{121}{8})}[/tex]
