[tex]1.\\f(x)=-2x^2+7\\\Delta=0^2-4*(-2)*7\\\Delta=0+56\\\Delta=56\\p=\frac{-0}{2*(-2)}=0\\q=\frac{-56}{4*(-2)}=\frac{-56}{-8}=7\\W(0; 7)\\Odp. C[/tex]
[tex]2.\\f(x)=x^2-3\\\Delta=0^2-4*1*(-3)\\\Delta=12\\q=\frac{-12}4=-3\\a>0 - \text{ramiona skierowane w gore}[/tex]
Zw∈<-3; ∞)
Odp. A
[tex]3. \\f(x)=-2x^2-4x-1\\f(-2)=-2*(-2)^2-4*(-2)-1\\f(-2)=-2*4+8-1\\f(-2)=-8+8-1\\f(-2)=-1\\Odp. C[/tex]
[tex]4. \\y=-2x^2+4x-6\\p=\frac{-4}{2*(-2)}=\frac{-4}{-4}=1\\x=1\\Odp. D[/tex]
[tex]5. \\f(x)=(x+5)^2-3\\W(-5; -3)\\f(-5)=-3\\Odp. D[/tex]
[tex]6. \\y=4x^2+bx+c\\x_1=5\\x_2=-3\\\\\left \{ {{0=4*5^2+5b+c} \atop {0=4*(-3)^2-3b+c}} \right. \\\left \{ {{0=4*25+5b+c} \atop {0=4*9-3b+c}} \right. \\\left \{ {{-100=5b+c /*3} \atop {-36=-3b+c /*5}} \right. \\+\left \{ {{-300=15b+3c} \atop {-180=-15b+5c}} \right. \\-300-180=3c+5c\\-480=8c /:8\\-60=c\\-100=5b-60 /+60\\-40=5b /:5\\-8=b\\\\Odp. A[/tex]
7.A tresc?
8. Brak tresci
9.
[tex]-3x^4+2x^3-x+2=-3*(-1)^4+2*(-1)^3-(-1)+2=\\-3*1+2*(-1)+1+2=\\-3-2+1+2=\\-5+3=-2\\Odp. C[/tex]
[tex]10. \\(x^4-x^2+2)(2-3x-5x^2)(3-2x)=\\(2x^4-3x^5-5x^6-2x^2+3x^3+5x^4+4-6x-10x^2)(3-2x)=\\(-5x^6-3x^5+7x^4+3x^3-12x^2-6x+4)(3-2x)=\\-15x^6+10x^7-9x^5+6x^6+21x^4-14x^5+9x^3-6x^4-36x^2+24x^3-18x+12x^2+12-8x=\\10x^7-9x^6-23x^5+15x^4+33x^3-24x^2-26x+12[/tex]
Odp. A
