Graphing x²/16 - y²/9 = 1

Algebra 2 · Axiom Academy

Identify the hyperbola's transverse axis, vertices, and asymptotes from standard form, then sketch its graph. Identify the key features of the hyperbola — its transverse axis, vertices, and asymptotes — then sketch its graph. Center (0,0) , a=4 , b=3 — plotted with the vertices, the auxiliary box, the asymptotes, and both branches. Nice work — you graphed a hyperbola straight from its equation. The pieces worth keeping: Standard form: for a horizontal hyperbola — the POSITIVE term names the transverse axis. Transverse axis: runs through the vertices, length 2a . Conjugate axis: perpendicular to it, length 2b — it doesn't touch the curve, but it sets the box the asymptotes come from. Vertices: for a horizontal hyperbola, for a vertical one. Asymptotes: for horizontal — the extended diagonals of the central box. This hyperbola: a=4 , b=3 , vertices , asymptotes . The branches hug the asymptotes more and more closely the farther out you go — but they approach, never touch.

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