Dobierz wzór do wykresu wielomianu stopnia czwartego
Na rysunku przedstawiono wykres wielomianu stopnia czwartego.
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text-anchor="end">−4</text><text x="138" y="109.5" text-anchor="end">−2</text><text x="138" y="65.5" text-anchor="end">2</text><text x="138" y="43.5" text-anchor="end">4</text></g><g fill="currentColor" font-size="12" opacity="0.85" stroke="var(--bg-page)" stroke-width="2" paint-order="stroke"><text x="314" y="77" text-anchor="end">x</text><text x="151" y="22">y</text></g><g fill="currentColor" stroke="var(--bg-page)" stroke-width="2" paint-order="stroke"><text x="151" y="121" font-size="10.5">(0, −3)</text></g> Który wzór opisuje ten wielomian?
A. B.
C. D.
Rozwiązanie
Pokaż rozwiązanie krok po krokuUkryj rozwiązanie
Krok 1. Miejsca zerowe. Wykres przecina oś w i , a w jej dotyka. Potrzebne są więc czynniki , i w potędze parzystej - stąd . Wzór A ma miejsca zerowe , , (znaki odwrócone) - odpada.
Krok 2. Krańce wykresu. Oba końce idą w górę: stopień parzysty i współczynnik wiodący dodatni. Wzór C ma współczynnik , czyli oba końce w dół - odpada.
Krok 3. Punkt na osi . Zostały B i D, różniące się tylko współczynnikiem. Rozstrzyga punkt :
Tylko B daje .
Uwaga: same miejsca zerowe i kształt nie wystarczają - wzory B i D mają identyczne miejsca zerowe i krańce. Współczynnik wyznacza dopiero dodatkowy punkt.
Odpowiedź. B: .
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