Wzór wielomianu stopnia 3 odczytany z wykresu
Na rysunku przedstawiono wykres wielomianu stopnia trzeciego.
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text-anchor="middle">2</text><text x="177" y="201.5" text-anchor="end">−10</text><text x="177" y="181.5" text-anchor="end">−8</text><text x="177" y="161.5" text-anchor="end">−6</text><text x="177" y="141.5" text-anchor="end">−4</text><text x="177" y="121.5" text-anchor="end">−2</text><text x="177" y="81.5" text-anchor="end">2</text><text x="177" y="61.5" text-anchor="end">4</text><text x="177" y="41.5" text-anchor="end">6</text></g><g fill="currentColor" font-size="12" opacity="0.85" stroke="var(--bg-page)" stroke-width="2" paint-order="stroke"><text x="322.5" y="91" text-anchor="end">x</text><text x="190" y="22">y</text></g><g fill="currentColor" stroke="var(--bg-page)" stroke-width="2" paint-order="stroke"><text x="190" y="142" font-size="10.5">(0, −4)</text></g> Wyznacz wzór wielomianu w postaci iloczynowej i w postaci ogólnej.
Rozwiązanie
Pokaż rozwiązanie krok po krokuUkryj rozwiązanie
Krok 1. Odczyt miejsc zerowych. W wykres przecina oś - krotność nieparzysta. W dotyka osi - krotność parzysta, co najmniej . Stopień wynosi , więc krotności to dokładnie i :
Krok 2. Współczynnik z punktu .
Krok 3. Postać ogólna. Najpierw , potem
Krok 4. Kontrola z wykresem. Współczynnik wiodący przy stopniu nieparzystym: lewy koniec w górze, prawy w dole - tak jak na rysunku. Dodatkowo , co zgadza się z najniższym punktem wykresu między a .
Odpowiedź. .
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