Exam 10: Completing the Square

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Solve the equation. Solve the equation.   x = __________ x = __________

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Solve the inequality and graph the solution set. Solve the inequality and graph the solution set.

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Solve the following quadratic equation by completing the square. Solve the following quadratic equation by completing the square.   x = __________ x = __________

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Determine Determine   so that the following equation has exactly one real solution.  so that the following equation has exactly one real solution. Determine   so that the following equation has exactly one real solution.

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Solve the inequality and graph the solution set. Solve the inequality and graph the solution set.

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Use the discriminant to find the number and kind of solutions for the following equation. Use the discriminant to find the number and kind of solutions for the following equation.   Discriminant   __________ How many solutions does the equation have? __________ What kind of solutions are they? __________ Discriminant Use the discriminant to find the number and kind of solutions for the following equation.   Discriminant   __________ How many solutions does the equation have? __________ What kind of solutions are they? __________ __________ How many solutions does the equation have? __________ What kind of solutions are they? __________

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Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square. Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.   _____   _____  _____ Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.   _____   _____  _____ Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.   _____   _____

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Use the discriminant to find the number and kind of solutions for the following equation. Use the discriminant to find the number and kind of solutions for the following equation.   Discriminant   __________ How many solutions does the equation have? __________ What kind of solutions are they? __________ Discriminant Use the discriminant to find the number and kind of solutions for the following equation.   Discriminant   __________ How many solutions does the equation have? __________ What kind of solutions are they? __________ __________ How many solutions does the equation have? __________ What kind of solutions are they? __________

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Solve the inequality and graph the solution set. Solve the inequality and graph the solution set.

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Simplify. Simplify.

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Multiply both sides of the equation by their LCD. Then solve the resulting equation. Multiply both sides of the equation by their LCD. Then solve the resulting equation.   r = __________ r = __________

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Find an equation that has the given solutions. Find an equation that has the given solutions.   ,  , Find an equation that has the given solutions.   ,

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Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)

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An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance s it travels and time t is given by An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance s it travels and time t is given by   . How long does it take the object to fall 70 feet? __________ second(s) . How long does it take the object to fall 70 feet? __________ second(s)

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Use the discriminant to find the number and kind of solutions for the following equation. Use the discriminant to find the number and kind of solutions for the following equation.

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Solve the equation. Solve the equation.   y = __________ y = __________

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For the equation, find the coordinates of the vertex, and indicate whether the vertex is the highest point on the graph or the lowest point on the graph. (Do not graph.) For the equation, find the coordinates of the vertex, and indicate whether the vertex is the highest point on the graph or the lowest point on the graph. (Do not graph.)   Vertex = __________ The vertex is the __________ point on the graph. Vertex = __________ The vertex is the __________ point on the graph.

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Solve the equation. Solve the equation.   x = __________ x = __________

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Find an equation that has the given solutions. Find an equation that has the given solutions.   ,  , Find an equation that has the given solutions.   ,

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Solve the equation. Solve the equation.   x = __________ x = __________

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