Questions and Answers
What is the rule for g(x) if it is a vertical translation of f(x) = -4x + 8, 3 units down?
4x + 5
What is the rule for g(x) if it involves a vertical shift of f(x) = -x up 4 units followed by a vertical stretch by a factor of 3?
-x + 4
What is the maximum distance the skateboard can travel according to the function d(t) = 4.9t^2 - 2.3t + 5, and at what time?
4.73 meters at 0.23 seconds
What are the roots of the equation 30x - 45 = 5x^2?
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Complete the square for the expression x^2 - 16x + _____
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What is the solution to the equation 2x^2 + 18 = 0?
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What is the complex conjugate of 3i + 4?
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What is the number and type of solutions for the inequality x^2 - 14x + 4 > -11?
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Solve the inequality -8x^2 - 14x + 4 > -11.
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Study Notes
Transformation of Functions
- For g(x) as a vertical translation of f(x) = -4x + 8, resulting in a shift down 3 units: g(x) = -4x + 5.
- g(x) represents a vertical shift of f(x) = -x up 4 units followed by a vertical stretch by a factor of 3: g(x) = -x + 4.
Motion of Skateboard on a Ramp
- The function d(t) = 4.9t² - 2.3t + 5 models the distance d (in meters) traveled by a skateboard over time t (in seconds).
- The maximum distance achieved by the skateboard is 4.73 meters at 0.23 seconds.
Factoring Quadratic Equations
- To find the roots of the equation 30x - 45 = 5x² by factoring, the solution is x = 3.
Completing the Square
- For the expression x² - 16x + _____, the completed square form is (x - 8)².
Solving Quadratic Equations
- The equation 2x² + 18 = 0 has solutions in the complex number realm: x = ±3i.
Complex Conjugates
- The complex conjugate of 3i + 4 is found to be 4 - 3i.
Solutions to Inequalities
- The inequality x² - 14x + 4 > -11 indicates there are two solutions.
- For solving -8x² - 14x + 4 > -11, the solution is x < -2.5.
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Description
Prepare for your Algebra 2 final exam with this study guide consisting of flashcards. Each card presents key concepts such as transformations of functions and distance-time relationships. Test your understanding and apply the rules to solve the given problems.
