Hyperbolas
In the following problems, determine the standard equation of each hyperbola.
Hint: Group the variables with like terms together and complete the square twice.
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| 1) Write the standard equation of the hyperbola.
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| 2) Write the standard equation of the hyperbola.
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| 3) Write the standard equation of the hyperbola.
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In the following problems, state the center. Then state whether the hyperbola opens up and down or left and right.
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| 4) State the center. Then state whether the hyperbola opens up and down or left and right.
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| 5) State the center. Then state whether the hyperbola opens up and down or left and right.
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| 6) State the center. Then state whether the hyperbola opens up and down or left and right.
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Solving Quadratic Systems of Equations
In the following problems, solve the system of equations. State the answers as ordered pairs.
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| 7) Use substitution to solve the system.
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| 8) Use substitution to solve the system.
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| 9) Use elimination to solve the system.
Hint: Multiply each equation in the first term by –1 and then add the terms together.
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| 10) Use elimination to solve the system.
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Conic Sections
In the following problems, classify each equation as a circle, ellipse, hyperbola, or parabola.
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| 11) Circle, ellipse, hyperbola, or parabola?
(x – 3)2 + (y + 2)2 = 81
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| 12) Circle, ellipse, hyperbola, or parabola?
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| 13) Circle, ellipse, hyperbola, or parabola?
x2 + 4x + y2 + 7y = 15
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| 14) Circle, ellipse, hyperbola, or parabola?
x2 – 2x + 3y2 – 2y – 6 = 0
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| 15) Circle, ellipse, hyperbola, or parabola?
4y2 – 12y – x2 – 2x – 4 = 0
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| 16) Circle, ellipse, hyperbola, or parabola?
y2 – 3x = 9y – 4
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| 17) Circle, ellipse, hyperbola, or parabola?
4x2 – 35 = 50y – 16y2
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| 18) Solve the absolute value equation for “x”.
Hint: This question has two answers.
Click here to review the unit content explanation for Inequalities and Absolute Value Equations.
| x – 7 | = 9
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| 19) Simplify.
Click here to review the unit content explanation for Operations with Numbers and Exponents.
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| 23) Write the expression as a single logarithm and then simplify, if possible.
Hint: Use the properties of logarithms.
Click here to review the unit content explanation for Logarithmic Functions.
3log52 – 2log53
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| 24) Find the difference.
Click here to review the unit content explanation for Polynomial Functions.
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| 25) Solve for “x”.
Click here to review the unit content explanation for Radical Expressions and Equations.
Hint: Square both sides of the equation and then solve for x.
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| 26) Extended Learning
Watch the following video, then write a five-sentence paragraph summarizing the video.
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| 27) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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