Odpowiedź:
1. a=5, b=3, c=7
2. P, P
3. a) Δ=[tex](-10)^{2} -4*2*(-5)=100+50=140[/tex]
b) Δ=[tex]8^{2} -4*(-4)*(-7)=64-112=-48[/tex]
4.
[tex]y= -5(x^{2} -2x+1)+3\\y=-5x^{2} +10x-5+3\\y=-5x^{2} +10x-2[/tex]
5.w=(p,q)
Δ=[tex]64-40=24[/tex]
[tex]p=\frac{-b}{2a} = \frac{8}{4} = 2[/tex]
[tex]q=\frac{-delta}{4a} = \frac{-24}{8} = -3[/tex]
w=(2,-3) odp. B
6. a) Δ=25+96=121
√Δ=11
[tex]x=\frac{-5-11}{4} = \frac{-16}{4} = -4[/tex]
[tex]x=\frac{-5+11}{4} = \frac{6}{4} = \frac{3}{2}[/tex]
odp. x=-4, x=3/2
7. a) 2x^2-8=0
2x^2=8 /:2
x^2=4
x=2, x=-2
b) 9-x^2=0
x^2=9
x=3, x=-3
8. miejsca zerowe x=0, x=2
W=(1, -1)
9. Δ= 225+400=625
√Δ=25
[tex]x=\frac{-15-25}{-10}=\frac{-40}{-10}=4\\x=\frac{-15+25}{-10}=\frac{10}{-10} = -1[/tex]
ramiona paraboli skierowane są w dół
odp. x∈<-1, 4>
