Calculus I - Common Graphs

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Section 1.10 : Common Graphs

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18. Without using a graphing calculator sketch the graph of \(\displaystyle {\left( {y + 2} \right)^2} - \frac{{{{\left( {x + 4} \right)}^2}}}{{16}} = 1\).

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This is a hyperbola in standard form with the minus sign in front of the \(x\) term and so will open up and down. The center of the hyperbola is at \(\left( { - 4, - 2} \right)\), the two vertices are at \(\left( { - 4, - 1} \right)\) and \(\left( { - 4, - 3} \right)\), and the slope of the two asymptotes are \( \pm \frac{1}{4}\).

Here is a quick sketch of the hyperbola.