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1.3 Completing the Square

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1.3 Completing the Square

1. 1. 1.3 Completing the Square February 13, 2013 Mental Math Factor x2 ­ 14x + 49 Expand (x ­ 3)2
2. 2. 1.3 Completing the Square February 13, 2013 1.3 Coverting Standard Form to Vertex Form It is fairly laborious to draw the graph of a parabola from the standard form (you have to remember x = -b/2a, find points, etc). It is easier to convert to vertex form from standard form. we do ! y = ax2 + bx + c w Ho do it? Complete the Square! y = a(x - p)2 + q What does completing the square mean? y = a(x - p)2 + q } Perfect square trinomial: a2 - 2ab + b2 = (a - b)2 or a2 + 2ab + b2 = (a + b)2
3. 3. 1.3 Completing the Square February 13, 2013 We want to make a perfect square trinomial out of the first two terms in the standard form y = ax2 + bx + c } Use these two terms to make the perfect square trinomial Review: Perfect Square Trinomial x2 + 10x + 25 4y2 - 28y + 49
4. 4. 1.3 Completing the Square February 13, 2013 Lets use algebra tiles to visualize whats going on... Complete the square: x2 - 6x x2 x -x How many of the yellow boxes do we need to add to 1 the box to complete the -1 square? Algebraically: y = x2 - 6x
5. 5. 1.3 Completing the Square February 13, 2013 When using completing the square to convert standard form to vertex form, we need to make sure that were not breaking the (math) universe by creating an unbalance situation. Convert to standard form: y = x2 - 6x x2 ** What have we done to create an unbalanced equation?? x -x We added 9; at this point, we need 1 to balance our equation by subtracting 9 as -1 well
6. 6. 1.3 Completing the Square February 13, 2013 Convert to standard form: y = x2 - 6x + 10 x2 x -x 1 -1 Lets do this algebraically y = x2 - 6x + 10 Step 1. Group the x-terms together. Step 2. Add a last term that would complete the perfect square trinomial
7. 7. 1.3 Completing the Square February 13, 2013 Lets do this algebraically y = x2 - 6x + 10 Step 3. Obey the Laws of Math!! Step 4. Factor the perfect trinomial
8. 8. 1.3 Completing the Square February 13, 2013 E.g. Convert y = x2 + 16x - 5 to vertex form
9. 9. 1.3 Completing the Square February 13, 2013 Convert to vertex form and verify: y = ­3x ­ 24x + 19 2 ** This time we have a problem, we have a term in front of the 2x
10. 10. 1.3 Completing the Square February 13, 2013 Rylee has 12m of edging to place along the three sides of the  garden to separate it from her lawn. What dimensions will give the  maximum area for the garden? Homework Page 192-193 #1-4