Download 4.7 Notes Completing the Square Algebra 2 Perfect Square

4.7 Notes
Algebra 2
Completing the Square
Perfect Square Trinomial -
x2  8x 16 
2
b

b
x  bx  x  bx      x  
2
 2

2
x2 12x  36 
2
2
Example: x2  6 x 
Example 1: Find the value of c that makes x 2  20x  c a perfect square trinomial.
Example 2: Find the value of c that makes x2  7 x  c a perfect square trinomial.
How to solve an equation by completing the square: x2 10x  3  0 .
1. Write the original equation:
**The coefficient of x2 must be 1!!! If not,
you must factor it out first!
2. Move the c value over to the other side. The
equation should be in the form of x2  bx = c.
2
b
3. Add   to both sides.
2
4. Rewrite the left side as the square of a binomial
5. Take the square roots of each side.
6. Finish solving for x.
Example 4: x2  6x  8  0
Example 5: 3x2  6x 12  0
Example 6: Rewriting an equation from standard form to vertex form: y  a  x  h   k
2
A) y  x2  8x 11
4.7 # 14 – 32 even, 41 - 43
B.) y  x2  6 x 16
C.) y  x2  3x  3