Warm-Up, Completing the Square In #1-2, fill in the missing part of the picture using squares of about this size: to turn the big figure shown into a square.

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Presentation transcript:

Warm-Up, Completing the Square In #1-2, fill in the missing part of the picture using squares of about this size: to turn the big figure shown into a square. # of small squares needed: ______ In #3-5, factor. 3. x 2 + 8x x 2 + 6x x x + 64 (X+4) 2 (X+3) 2 (X-8)

Warm-Up Part II: Match the Solutions to the Graphs a. x =-2 or 31. b. x = 42. c. x = {2+i}3. d. x = { } 4. c. (no real solutions) a. It hits the x-axis at -2 and 3. b. It hits the x-axis at 4 only. d. It hits the x-axis at about 3 and 7. Adapted from resources at:

► Completing the square can be used for non-factorable problems. ► What would make these trinomials perfect squares? ► What do they become in factored form? Objectives: To create perfect square trinomials. To solve quadratics by completing the square.

Find half the coefficient of the middle term and square it. So, it factors into this! You have created a perfect square trinomial (PST). Completing the Square

Write the expression in factored form, then find the value that makes this expression a perfect square trinomial. f) x 2 -3x+___

Complete the square to solve. g) x 2 +6x-8=0 x 2 +6x=8 x 2 +6x+___=8+___ (x+3) 2 1.Move the constant to the other side. 2.Divide all terms by the leading coefficient (the number with x 2 ). 3.Create a blank on each side. 4.Complete the square. Find half the coefficient of the x (middle) term.Find half the coefficient of the x (middle) term. Use that number to rewrite the trinomial as a perfect square.Use that number to rewrite the trinomial as a perfect square. Square the number you found.Square the number you found. Fill that value into each blank.Fill that value into each blank. 5. Solve for x. Start by square rooting each side.Start by square rooting each side. = 17

► h) 5x 2 -10x+30=0 x 2 -2x+6=0 x 2 -2x+__=-6+__ (x-1) 2 ► j) 3x 2 -12x-24=0 x 2 -4x-8=0 x 2 -4x+__=8+__ (x-2) 2 You cannot have a leading coefficient! =-5 =12

What if it doesn’t divide out so easily? k) 3x 2 +8x+16=0 3x 2 +8x = -16 3x 2 +8x = -16 Still divide by the leading coefficient! Still divide by the leading coefficient!

…continued SOLVE: SOLVE: Square root both sides. Square root both sides. Simplify. Simplify. Get x alone. Get x alone.