Today:
Warm-Up: Number Sense
Warm-Up: Review Quadratic Graphs
Introduction to Completing the Square
Class Work
1
Number Sense: Time
It is 12:00 noon on a February Friday in
Saipan. What time and day is it in...
1. Tokyo, Japan
4. Honol...
4. 90% of 90 girls and 80%
of 110 boys have shown up
at the stadium on time.
How many people are late?
Warm-Up:
3
Warm-Up:
5. If the parabola y = x2 is flipped upside down, made 5
times as wide, and shifted 8 units down the y-axis,
writ...
Class Notes Section of Notebook
5
6
Solve by Taking Square Root:
7
Solve by Taking Square Root:
8
Completing the Square:
9
10
Completing the Square
Factoring “unfactorable” 2nd degree trinomials
11
• We have learned earlier that a perfect square trinomial
can always be factored.
• Therefore, if we have a trinomial w...
12
• Recall that a perfect square trinomial is always in the
form:
• Therefore, we have to change the polynomial so that i...
13
The equation we are going to solve is the following…
By testing whether or not the factors of c can sum to equal
b, we ...
Step 1
Divide by the leading coefficient
to set the a-value to 1.
14
2
2
2 16 20 0
2
8 10 0
x x
x x
Completing the Square:
Step 2 Re-write the equation
in the form ax + by = c
15
2
2
2
8 10 0
8 10 10 10
18 0
0
x x
x x
x x
Completing the Square:
Step 3 Find one-half of the b value.
Add the square of that number to
both sides.
16
2
2
2
2 2
8 10
8 104 4
16 28 6
x x
x ...
Step 4
A) Re-write the perfect square
trinomial as a binomial squared.
B) Find the square root of each side
of the equatio...
Step 5 Solve for x.
18
4 2
4
2
6
264
6
4
4
x
x
x
Completing the Square:
19
Completing the Square:
Example 2
x2
- 16x +15 = 0
Re-write the equation in
the form ax + by = c
Divide by leading coeff...
1) Find the value of
2
2
b
2
x bx
Completing the Square:
2. Add the value to the
expression, this completes
the square
2
6...
Solving an Equation by
Completing the Square
Class Work:
See Handout
22
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April 10

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April 10

  1. 1. Today: Warm-Up: Number Sense Warm-Up: Review Quadratic Graphs Introduction to Completing the Square Class Work 1
  2. 2. Number Sense: Time It is 12:00 noon on a February Friday in Saipan. What time and day is it in... 1. Tokyo, Japan 4. Honolulu, Hawaii3. South Pole, Antarctica 2. New York, NY 1. Friday, 11:00 am 4. Thursday, 4:00 pm3. Friday, 3:00 pm 2. Friday, 3:00 am
  3. 3. 4. 90% of 90 girls and 80% of 110 boys have shown up at the stadium on time. How many people are late? Warm-Up: 3
  4. 4. Warm-Up: 5. If the parabola y = x2 is flipped upside down, made 5 times as wide, and shifted 8 units down the y-axis, write the equation for the new parabola. 6. If the parabola y = x2 is flipped upside down, made twice as narrow, and shifted 6 units up the y-axis, write the equation for the new parabola. y = -⅕x2 - 8 y = -2x2 + 6 4
  5. 5. Class Notes Section of Notebook 5
  6. 6. 6
  7. 7. Solve by Taking Square Root: 7
  8. 8. Solve by Taking Square Root: 8
  9. 9. Completing the Square: 9
  10. 10. 10 Completing the Square Factoring “unfactorable” 2nd degree trinomials
  11. 11. 11 • We have learned earlier that a perfect square trinomial can always be factored. • Therefore, if we have a trinomial we cannot factor using integers, we can change it in such a way that we are dealing with a perfect square trinomial. Completing the Square:
  12. 12. 12 • Recall that a perfect square trinomial is always in the form: • Therefore, we have to change the polynomial so that it fits the form. • To really learn this, go through each step of the process. Your goal should be to learn the steps in order. 22 2 baba Completing the Square:
  13. 13. 13 The equation we are going to solve is the following… By testing whether or not the factors of c can sum to equal b, we can determine if the trinomial is factorable. This trinomial is not factorable in its present form. However, with our new tool, we can solve this previously 'unsolvable' quadratic. 2 2 16 20 0x x There are five steps in this process, let's write them down. Completing the Square:
  14. 14. Step 1 Divide by the leading coefficient to set the a-value to 1. 14 2 2 2 16 20 0 2 8 10 0 x x x x Completing the Square:
  15. 15. Step 2 Re-write the equation in the form ax + by = c 15 2 2 2 8 10 0 8 10 10 10 18 0 0 x x x x x x Completing the Square:
  16. 16. Step 3 Find one-half of the b value. Add the square of that number to both sides. 16 2 2 2 2 2 8 10 8 104 4 16 28 6 x x x x x x 2 2 b Completing the Square:
  17. 17. Step 4 A) Re-write the perfect square trinomial as a binomial squared. B) Find the square root of each side of the equation. 17 2 2 4 8 16 26 26 264 x x x x Completing the Square:
  18. 18. Step 5 Solve for x. 18 4 2 4 2 6 264 6 4 4 x x x Completing the Square:
  19. 19. 19 Completing the Square: Example 2 x2 - 16x +15 = 0 Re-write the equation in the form ax + by = c Divide by leading coefficient x2 - 16x = -15 2 2 bTake one-half of b, then square it. Add the square to both sides. x2 - 16x + 64 = -15 + 64 Simplify both sides.x2 - 16x + 64 = -15 + 64 (x - 8)2 = 49
  20. 20. 1) Find the value of 2 2 b 2 x bx Completing the Square: 2. Add the value to the expression, this completes the square 2 6x x 2 10x x
  21. 21. Solving an Equation by Completing the Square
  22. 22. Class Work: See Handout 22

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