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Geometria e aritmetica » Le parabole

Geometria e aritmetica

In matematica abbiamo studiato le parabole, con le relative proprietà e la loro equazione.

Abbiamo visto che l’equazione è Ax2+Bx+C=y, e con essa è stato possibile studiare e approfondire molti aspetti e/o proprietà della parabola.

Abbiamo poi visto le proprietà, tra le quali le più importanti, anche per uno pratico, sono sicuramente che tutti i raggi paralleli all’asse ottico rimbalzano sulla parabola e confluiscono nel fuoco e che tutti i raggi che partono dal fuoco e rimbalzano sulla parabola viaggiano paralleli all’asse ottico, e questo è il motivo per cui se si posiziona un oggetto sul fuoco di uno specchio a forma di parabola, l’immagine risultante è infinita.

Disegnare una parabola dall’equazione

Per disegnare una parabola da un’equazione y=ax2+bx+c, bisogna per prima cosa determinare i valori di a,b e c. Ad esempio: y=x2+2x-3 a=+1 b=+2 c=-3 Ora dobbiamo trovare le coordinate x,y del vertice, seguendo le formule: Xv=-b/2a Yv=-(b2-4ac)/4a Quindi il V nell’equazione precedente sarà: Xv=-2/2=-1 Yv=-(4+12)/4=-4 V(-1;-4) Successivamente va trovato i punti della parabola posti sull’asse …

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IMG-CP-6

Disegnare una parabola qualsiasi

Per disegnare una parabola qualsiasi bisogna seguire la procedura sottostante, che serve a trovare un punto appartenente a essa, per poi trovarne svariati e unirli con un curvilinee, per ottenere in fine una parabola. Procedura Disegnare una retta direttrice e un punto F a piacere. Disegnare un punto H appartenente alla direttrice. Tracciare una retta …

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Parabole con geogebra

Per approfondimenti sul programma: Sito ufficiale Wikipedia – Geogebra Alcuni esempi e tutorial Indice 1° immagine 2° immagine 3° immagine 1° immagine Questo è un’”immagine” dinamica, in quanto consente di muovere il punto H per poter verificare la parabola in qualsiasi punto. Questa è un’Applet Java creata con GeoGebra da www.geogebra.org – Java non risulta …

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