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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.137 (page 1119)

In the following exercise, graph the equation $y = 6 x^{2} + 2 x - 1$

Short Answer

Expert verified

The required standard equation and graph is ${(x + \frac{1}{6})}^{2} = \frac{1}{6} (y + \frac{7}{6})$

Step by step solution

01

Step 1, Given the information

The given equation of the curve $y = 6 x^{2} + 2 x - 1$

02

Step 2. Convert into a standard form

$y = 6 x^{2} + 2 x - 1 y = 6 (x^{2} + 2 . \frac{x}{6} - \frac{1}{6}) y = 6 (x^{2} + 2 . \frac{x}{6} + \frac{1}{36} - \frac{1}{36} - \frac{1}{6}) y = 6 {(x + \frac{1}{6})}^{2} - 1 - \frac{1}{6} y = 6 {(x + \frac{1}{6})}^{2} - \frac{7}{6} 6 {(x + \frac{1}{6})}^{2} = y + \frac{7}{6} {(x + \frac{1}{6})}^{2} = \frac{1}{6} (y + \frac{7}{6})$

which is a parabola

03

Step 3. Draw a graph

The standard equation of a parabola is ${(x + \frac{1}{6})}^{2} = \frac{1}{6} (y + \frac{7}{6})$

Whose vertex is $(\frac{- 1}{6}, - \frac{7}{6})$

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