Matematica - Ecuatii si inecuatii. Functii

Ecuatii si inecuatii. Functii - Intrebarea 19

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Să se determine ecuaţia de gradul al doilea al cărei grafic este tangent la axa $O x$ în punctul de coordonate $left parenthesis negative 1 comma 0 right parenthesis$ şi trece prin punctul de coordonate $left parenthesis 0 comma 1 right parenthesis$ .

f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals 2 x squared plus 2 x plus 1

f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals x squared plus 2 x plus 1

f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals x squared plus 2 x plus 2

Raspunsul este corect.

Raspunsul este gresit.

Explicatie:

Răspuns corect: B

Fie $f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals a x squared plus b x plus c comma space a comma b comma c element of straight real numbers comma space a not equal to 0.$

Avem:

$M left parenthesis 0 comma 1 right parenthesis element of G subscript f left right double arrow f left parenthesis 0 right parenthesis equals 1 rightwards double arrow c equals 1 N left parenthesis negative 1 comma 0 right parenthesis element of G subscript f left right double arrow f left parenthesis negative 1 right parenthesis equals 0 rightwards double arrow a minus b equals negative 1 increment equals 0 left right double arrow b squared minus 4 open parentheses negative 1 plus b close parentheses equals 0 rightwards double arrow b equals 2 rightwards double arrow a equals 1.$

Funcţia căutată este: $f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals x squared plus 2 x plus 1$ .