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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 164E (page 1134)

In the following exercises, graph.
$\frac{{(y + 1)}^{2}}{16} - \frac{{(x + 1)}^{2}}{4} = 1$

Short Answer

Expert verified

The graph is as below

Step by step solution

01

Step 1. Given information

The equation is $\frac{{(y + 1)}^{2}}{16} - \frac{{(x + 1)}^{2}}{4} = 1$

Draw the graph.

02

Step 2. Calculation

The y² term is positive, the transverse axis is vertical.

The hyperbola opens up and down.

Find the centre

Compare the equation with standard form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$

So, $(h, k) = (- 1, - 1)$ and $a^{2} = 16 鈬� a 卤 4$ ,

$b^{2} = 4 鈬� b 卤 2$

Sketch the rectangle that goes through the points 4 units above/below the centre

2 units left/right of centre

03

Step 3. Draw the graph

Sketch the asymptotes and draw the graph .

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