College Algebra & Trigonometry, 2018a

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5.2. THE EQUATION OF THE PARABOLA 273 11) Focus: (0, 0) 12) Focus: (0, 0) Vertex: (0, −1.25) Vertex: (0, 2.5) 13) Focus: (2, 7) 14) Focus: (−3, 0) Directrix: x =0.5 Directrix: x = −2 15) Vertex: (3, −2), axis of symmetry parallel to x-axis, contains the point (7, 3) 16) Vertex: (−6, −6), axis of symmetry parallel to y-axis, contains the point (0, 0)
274 CHAPTER 5. CONIC SECTIONS - CIRCLE AND PARABOLA If we are given the equation of a parabola and need to find the vertex, focus and directrix, it is often helpful to put the equation in standard form. This usually requires completing the square. If we’re given the equation: x 2 +6x − 4y +1=0 then we know that this will be either an upward or downward facing parabola. Let’s move everything away from the x terms but leave a space to complete the square: x 2 +6x =4y − 1 To complete the square on this, we need add 9 to both sides so that we can rewrite the left side as (x +3) 2 . x 2 +6x +9=4y − 1+9 (x +3) 2 =4y +8 Then we can factor out the coefficient of the y variable (even if it doesn’t factor evenly). (x +3) 2 =4(y +2) So, this is an upward facing parabola with the vertex at the point (−3, −2). To find the focus and directrix, we need to know the vlaue of p. Since 4p =4, then we know that p =1. This means that the focus will be 1 unit above the vertex at the point (−3, −1) and the directrix will be one unit below the vertex at the line y = −3. Vertex: (−3, −2) Focus: (−3, −1) Directrix: y = −3
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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14 CHAPTER 1. ALGEBRA REVIEW 1.2 Fa
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16 CHAPTER 1. ALGEBRA REVIEW Trinom
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20 CHAPTER 1. ALGEBRA REVIEW (3x ?)
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30 CHAPTER 1. ALGEBRA REVIEW Then,
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40 CHAPTER 1. ALGEBRA REVIEW devise
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44 CHAPTER 1. ALGEBRA REVIEW Exerci
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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140 CHAPTER 3. EXPONENTS AND LOGARI
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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204 CHAPTER 4. FUNCTIONS Now, if, i
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208 CHAPTER 4. FUNCTIONS Stretching
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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