{"paper":{"id":"site-2645","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":21,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2645/zad/3108","paper_id":"site-2645","number":"3108","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wskaż funkcję kwadratową, której zbiorem wartości jest przedział <-2,oo). A. y=-2x^2+2 B. y=-(x+1)^2-2 C. y=2(x-1)+2 D. y=(x+1)^2-2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3108.svg","solution_image":"img/site/2645/rozw-3108.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3109","paper_id":"site-2645","number":"3109","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykres funkcji kwadratowej f(x)=(x-3)^2-2 nie ma punktów wspólnych z prostą o równaniu A. y=-3 B. y=-1 C. y=1 D. y=3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3109.svg","solution_image":"img/site/2645/rozw-3109.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3110","paper_id":"site-2645","number":"3110","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wskaż równanie osi symetrii paraboli określonej równaniem y=-x^2+4x-11. A. x=-4 B. x=-2 C. x=2 D. x=4","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3110.svg","solution_image":"img/site/2645/rozw-3110.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3111","paper_id":"site-2645","number":"3111","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wskaż funkcję kwadratową, której zbiorem wartości jest przedział (-oo,3>. A. f(x)=-(x-2)^2+3 B. f(x)=(2-x)^2+3 C. f(x)=-(x+2)^2-3 D. f(x)=(2-x)^2-3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3111.svg","solution_image":"img/site/2645/rozw-3111.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3112","paper_id":"site-2645","number":"3112","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykres funkcji kwadratowej f(x)=3(x+1)^2-4 nie ma punktów wspólnych z prostą o równaniu A. y=1 B. y=-1 C. y=-3 D. y=-5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3112.svg","solution_image":"img/site/2645/rozw-3112.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3113","paper_id":"site-2645","number":"3113","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Prosta o równaniu y=a ma dokładnie jeden punkt wspólny z wykresem funkcji kwadratowej f(x)=-x^2+6x-10. Wynika stąd, że A. a=3, B. a=0, C. a=-1, D. a=-3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3113.svg","solution_image":"img/site/2645/rozw-3113.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/3114","paper_id":"site-2645","number":"3114","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Jaka jest najmniejsza wartość funkcji kwadratowej f(x)=x^2+4x-3 w przedziale <0,3>? A. -7, B. -4, C. -3, D. -2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-3114.svg","solution_image":"img/site/2645/rozw-3114.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/4347","paper_id":"site-2645","number":"4347","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"W układzie współrzędnych narysowano część paraboli o wierzchołku w punkcie A=(2,4), która jest wykresem funkcji kwadratowej f. Funkcja f może być opisana wzorem A. f(x) = (x-2)^2+4, B. f(x) = (x+2)^2+4, C. f(x) = -(x-2)^2+4, D. f(x) = -(x+2)^2+4","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-4347.svg","solution_image":"img/site/2645/rozw-4347.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5307","paper_id":"site-2645","number":"5307","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x)=a(x-1)(x-3). Na rysunku przedstawiono fragment paraboli będącej wykresem tej funkcji. Wierzchołkiem tej paraboli jest punkt W=(2,1). Współczynnik a we wzorze funkcji f jest równy A. 1; B. 2; C. -2; D. -1.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5307.svg","solution_image":"img/site/2645/rozw-5307.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5308","paper_id":"site-2645","number":"5308","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa $f$ jest określona wzorem f(x) = a(x-1)(x-3). Na rysunku przedstawiono fragment paraboli będącej wykresem tej funkcji. Wierzchołkiem tej paraboli jest punkt W = (2,1). Największa wartość funkcji f w przedziale <1,4> jest równa A. -3; B. 0; C. 1; D. 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5308.svg","solution_image":"img/site/2645/rozw-5308.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5309","paper_id":"site-2645","number":"5309","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x)=a(x-1)(x-3). Na rysunku przedstawiono fragment paraboli będącej wykresem tej funkcji. Wierzchołkiem tej paraboli jest punkt W=(2,1). Osią symetrii paraboli będącej wykresem funkcji f jest prosta o równaniu A. x=1; B. x=2; C. y=1; D. y=2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5309.svg","solution_image":"img/site/2645/rozw-5309.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5768","paper_id":"site-2645","number":"5768","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Zbiorem wartości funkcji kwadratowej f określonej wzorem f(x)=-(x+9)^2+m jest przedział \\nwod{-∞,-5}. Wtedy A. m=5 B. m=-5 C. m=-9 D. m=9","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5768.svg","solution_image":"img/site/2645/rozw-5768.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5769","paper_id":"site-2645","number":"5769","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Osią symetrii wykresu funkcji kwadratowej f określonej wzorem f(x) = 1/3x^2+4x+7 jest prosta o równaniu A. x=-6 B. y=-6 C. x=-2 D. y=-2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5769.svg","solution_image":"img/site/2645/rozw-5769.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/5770","paper_id":"site-2645","number":"5770","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Na rysunku poniżej przedstawiono fragment wykresu funkcji kwadratowej f określonej wzorem f(x) = ax² + bx + c. Stąd wynika, że A. {a<0 c<0 B. {a<0 c>0 C. {a>0 c<0 D. {a>0 c>0","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-5770.svg","solution_image":"img/site/2645/rozw-5770.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/6712","paper_id":"site-2645","number":"6712","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x)=3x^2+bx-5 dla każdej liczby rzeczywistej x. Współczynnik b jest liczbą rzeczywistą mniejszą od zera. Dokończ zdanie. Wybierz odpowiedź A, B albo C oraz jej uzasadnienie 1., 2. albo 3.Funkcja A. ma dwa rzeczywiste miejsca zerowe, ponieważ 1. b^2+60>0. B. ma jedno rzeczywiste miejsca zerowe, ponieważ 2. b^2+60=0. C. nie ma rzeczywistych miejsc zerowych, ponieważ 3. b^2+60<0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-6712.svg","solution_image":"img/site/2645/rozw-6712.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/6717","paper_id":"site-2645","number":"6717","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dana jest funkcja kwadratowa y=f(x), której fragment wykresu w kartezjańskim układzie współrzędnych (x,y) na rysunku poniżej. [rysunek] Funkcja kwadratowa y=f(x) jest określona wzorem A. y=-(x+5)^2-6 B. y=-(x+5)^2+6⋅r C. y=-(x-5)^2-6 D. y=-(x-5)^2+6","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-6717.svg","solution_image":"img/site/2645/rozw-6717.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/6879","paper_id":"site-2645","number":"6879","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Dana jest funkcja kwadratowa f określona wzorem y = f(x) = x² + 5x + 6 gdzie x∈ℝ Dokończ zdania. Zaznacz odpowiedź spośród A-D oraz odpowiedź spośród E-H. 1. Postać kanoniczna funkcji f wyraża się wzorem A. y=(x-5/2)² + 1/4 B. y=(x+5/2)² - 1/4 C. y=(x-1/4)² + 5/2 D. y=(x+1/4)² - 5/2 2. Postać iloczynowa funkcji f wyraża się wzorem E. y=(x-2)(x-3) F. y=(x-2)(x+3) G. y=(x+2)(x-3) H. y=(x+2)(x+3).","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-6879.svg","solution_image":"img/site/2645/rozw-6879.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/6885","paper_id":"site-2645","number":"6885","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x)=-2x^2+bx+c i przyjmuje wartości dodatnie tylko dla x∈(-4,2). Oceń prawdziwość poniższych stwierdzeń. Wybierz P, jeśli stwierdzenie jest prawdziwe, albo F - jeśli jest fałszywe. Osią symetrii paraboli będącej wykresem tej funkcji jest prosta x=1. P F. Postać iloczynowa funkcji f wyraża się wzorem f(x)=-2(x+4)(x-2). P F.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-6885.svg","solution_image":"img/site/2645/rozw-6885.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/7247","paper_id":"site-2645","number":"7247","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykresem funkcji kwadratowej f jest parabola o wierzchołku W=(5,7). Wówczas prawdziwa jest równość A. f(1)=f(9) B. f(1)=f(11) C. f(1)=f(13) D. f(1)=f(15)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-7247.svg","solution_image":"img/site/2645/rozw-7247.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/8149","paper_id":"site-2645","number":"8149","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x) = 2(x-2)² + 4. Oceń prawdziwość poniższych stwierdzeń. Wybierz P, jeśli stwierdzenie jest prawdziwe, albo F - jeśli jest fałszywe. Funkcja f ma dwa rzeczywiste miejsca zerowe. | P | F | W kartezjańskim układzie współrzędnych (x,y) osią symetrii wykresu funkcji f jest prosta o równaniu x=2. | P | F |","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-8149.svg","solution_image":"img/site/2645/rozw-8149.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2645/zad/8150","paper_id":"site-2645","number":"8150","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja kwadratowa f jest określona wzorem f(x) = 2(x-2)² + 4. Wzorem funkcji f zapisanym w postaci ogólnej jest A. f(x) = 2x² - 4 B. f(x) = 2x² + 12 C. f(x) = 2x² - 4x + 12 D. f(x) = 2x² - 8x + 12","answer":null,"answer_text":null,"solution":null,"image":"img/site/2645/zad-8150.svg","solution_image":"img/site/2645/rozw-8150.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}