9.5: COMPLETING THE SQUARE:
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9.5: COMPLETING THE SQUARE: Factoring: A process used to break down any polynomial into simpler polynomials. Zero-Product Property: For any real numbers a and b, If ab = 0 Then a = 0 or b = 0. Complete the square: A process where x2+bx can be changed into a perfect- square trinomial by adding
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Factoring: A process used to break down any polynomial into simpler polynomials. 9.5: COMPLETING THE SQUARE:. Zero-Product Property: For any real numbers a and b, If a b = 0 Then a = 0 or b = 0. - PowerPoint PPT Presentation
Transcript of 9.5: COMPLETING THE SQUARE:
9.5: COMPLETING THE SQUARE:Factoring: A process used to break down any polynomial into simpler polynomials.
Zero-Product Property: For any real numbers a and b, If ab = 0 Then a = 0 or b = 0.
Complete the square: A process where x2+bx can be changed into a perfect-square trinomial by adding
COMPLETE THE SQUARE: ax2 + bxProcedure:
1) Find the values of a and b.2) Use the formula of and add it to ax2 + bx.
3) Re-write ax2 + bx + as a product of perfect squares.
GOAL:
COMPLETE THE SQUARE:
Ex: What integer is needed to complete the square:
x2+5x+ ___?
SOLUTION: Following the steps given
2) (2.5)
3) x2+5x+6.25 (x+2.5)(x+2.5)
1) a = 1 and b = 5
x2+5x+ (2.5)
(x+2.5)
FINDING THE SOLUTION: (x+2.5) = 0
Using the Zero-Product property(x+2.5) = 0(x+2.5) = 0
X = -2.5 The solutions are x = -2.5 twice.If something happens twice we only touch the x-axis at that point.
COMPLETING THE SQUARE: ax2 + bx = C
Ex: What is the solutions of the equation:
x2+6X=216
SOLUTION:
2) (3)
3) x2+6x+9 (x+3)(x+3)
1) a = 1 and b = 6
x2+6x+(3)=216+(3)
(x+3)= 225 (x+3)= x = -3 x = -8, 2.
x2+6X=216
YOU TRY IT:
Ex: What are the solutions of:
r2-4r=30
SOLUTION:
2) (-2)
3) x2-4x+4 (x-2)(x-2)
1) a = 1 and b = -4
x2-4x+(-2)=30+(-2)
(x-2)= 34 (x-2)= x = 2 x = -3.8 and 7.8
R2-4r=30
REAL-WORLD:
You are plantingA flower gardenConsisting of 3 Square plots Surrounded by 1 ft border. The total area of the garden and the border is 100tf2.What is the side length x of each square plot?
SOLUTION:x +2
3x +2
A = b hA = (x +2)(3x +2)
100 = (x +2)(3x +2)
Adding an x to both sides of the picture we get:
100 = 3x2 + 8x + 4 FOIL
SOLUTION: To complete the square we now put it in the ax2+bx = c form:
100 = 3x2 + 8x + 43x2 + 8x = 100 - 43x2 + 8x = 96
We always prefer a to be 1, so divide by 3:
x2 + x =
SOLUTION: ContinueNow a = 1 , b =
3) x2 + x+ = +
1) x2 + x =
2)
(x + )(x+ )= +
VIDEOS: SOLVING BY
FACTORING Solving by factoring:
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring
VIDEOS: SOLVING BY
FACTORING Solving by factoring:
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-completing-the-square
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%202:%20Solving%20a%20quadratic%20equation%20by%20factoring
CLASSWORK:
Page 508-509:
Problems: 4, 7, 15, 21, 25, 36, 37.
