Algebra 2 4-6 Guided Practice: Completing the Square

by Matthew Richardson

| 14 Questions1

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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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36

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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.

- Complete the square by adding (\frac{b}{2})^2 to each side of the equation.
- Solve for x.
- Find square roots.
- Rewrite the equation in the form x^{2}+bx=c.
- 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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