[tex]Zad. 1\\f(x)=ax^2+bx+c\\\\x_1=-2\\x_2=4\\\\f(x)=a(x+2)(x-4)\\f(x)=a(x^2-4x+2x-8)\\f(x)=a(x^2-2x-8)\\f(x)=ax^2-2ax-8a\\\\A=(0, -4)\\\\-4=a*0^2-2*a*0-8a\\-4=-8a /:(-8)\\\frac12=a\\\\f(x)=\frac12x^2-2*\frac12*x-8*\frac12\\f(x)=\frac12x^2-x-4\\\\a=\frac12\\b=-1\\c=-4[/tex]
[tex]Zad. 2\\f(x)=2x^2-8x+3\\a=2\\a > 0 - \text{ ramiona paraboli skierowane w gore}\\p=\frac{8}{4}=2\\q=\frac{-((-8)^2-4*2*3)}{8}=\frac{-(64-24)}8=\frac{-40}8=-5\\p \in < 1; 4 > \\\\f(4)=2*4^2-8*4+3\\f(4)=2*16-32+3\\f(4)=32-32+3\\f(4)=3[/tex]
[tex]f_{min}=-5 \text{ dla }x =2\\f_{max}=3 \text{ dla } x=4[/tex]
