Algebra 2 4-6 Guided Practice: Completing the Square
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by Matthew Richardson
| 14 Questions
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Solve It! How can you use pieces like these to form a square with side length x + 3 (and no overlapping pieces)? Show a sketch of your solution on the canvas. Use bright contrasting colors.
You may also create a copy of this Google Drawing and use it for your model. If you do, upload a screenshot to the canvas.
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Take Note: Summarize the process of solving an equation that shows a perfect square trinomial equal to a constant.
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Problem 1 Got It?
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Problem 1 Got It?
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Problem 2 Got It? The lengths of the sides of a rectangular window have the ratio 1.6 to 1. The area of the window is 2822.4 in.². What are the window dimensions?
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Problem 3 Got It?
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Take Note: Summarize the process of completing the square.
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Problem 4 Got It? What value completes the square for the expression?

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Problem 4 Got It: Reasoning: Is it possible for more than one value to complete the square for an expression? Explain.
No; The in the expression for finding the value that completes the square, (b/2)², each input b provides exactly one output.
Yes; There will sometimes be both a positive and a negative value that completes the square for an expression.
Yes; There will sometimes be mutiple positive values that complete the square for an expression.
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Take Note: Place the steps for solving an equation by completing the square in the correct order.
  1. Complete the square by adding (\frac{b}{2})^2 to each side of the equation.
  2. Solve for x.
  3. Find square roots.
  4. Rewrite the equation in the form x^{2}+bx=c.
  5. Factor the trinomial.
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Problem 5 Got It?
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Take Note: Summarize the process of completing the square to rewrite a quadratic function in vertex form.
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Problem 6 Got It?
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Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?
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