solve.. question of the day ccgps geometry day 62 (10-24-13) unit question: how are real life...
TRANSCRIPT
Solve.
2
2
2
1. 5 13 6
2. 3 10 6
3. (x-2) 2 18
x x
x x
2
or 35
x x
4
or 23
x x
2or 6x x
Question of the Day
CCGPS GeometryDay 62 (10-24-13)
UNIT QUESTION: How are real life scenarios represented by quadratic functions?
Today’s Question:When is it useful to solve quadratics by completing the square?Standard: MCC9-12..A.REI.4b
Completing the Square
• Completing the square is used for all those not factorable problems!!
• It is used to solve these equations for the variable.
• It gets a little messy when a is not 1.
Perfect Square Trinomials
Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36
Creating a Perfect Square Trinomial
In the following perfect square trinomial, the constant term is missing. x2 + 14x + ____
Find the constant term by squaring half the coefficient of the linear term.
(14/2)2
x2 + 14x + 49
Perfect Square Trinomials
Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___
Example 1 Solving by Completing the Square
Solve the following equation by completing the square:
Step 1: Rewrite so all terms containing x are on one side.
2 8 20 0x x
2 8 20x x
Example 1 Continued
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.
2 8 =20 + x x
21( ) 4 then square it, 4 16
28
2 8 2016 16x x
Example 1 Continued
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
2 8 2016 16x x
2
( 4)( 4) 36
( 4) 36
x x
x
Step 4: Take the square root of each side.
2( 4) 36x
( 4) 6x
Example 1 Continued
Step 5: Solve for x. 4 6
4 6 an
d 4 6
10 and 2 x=
x
x x
x
Example 2 Solving by Completing the Square
Solve the following equation by completing the square:
Step 1: Rewrite so all terms containing x are on one side.
2 6 18 0 x x
2 6 18 x x
Example 2 Continued
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.
2 6 =18 + x x
21( ) 3 then square it, (-36 ) 9
2
2 6 189 9 x x
Example 2 Continued
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
2 6 189 9 x x
2
( 3)( 3) 27
( 3) 27
x x
x
Step 4: Take the square root of each side.
2( 3) 27 x
( 3) 3 3 x
Example 2 Continued
Step 5: Solve for x. 3 3 3 x
Solve each by Completing the Square
Solve each by Completing the Square
x2 + 4x – 4 = 0x2 – 2x – 1 = 0
Example 4 Finding Complex Solutions
x2 - 8x + 36 = 0 x2 +6x = - 34
Example 5 Solving When a≠0