1. Completing the Square. The Quadratic Formula.
What you’ll learn
To solve quadratic equations by factoring.
To solve quadratic equations by graphing.
To solve quadratic equations by completing the square.
To rewrite functions by completing then square
Vocabulary
Completing the square,
quadratic formula,
discriminant

2. Problem 1:What is the solution of each equation? A. B.
Completing the square
Note:
Completing a perfect square trinomial allows you to factor the completed trinomial as the square of a binomial. You can solve an equation that contains a perfect square by finding square roots. The simplest of this type of equation
Problem 1:What is the solution of each equation? A. B.

3. Your turn
What is the solution of each equation?
Answers :

4. Determining Dimensions
Problem 2:While designing a house, an architect used windows
like the one shown here. What are the dimensions of the
window if it has square inches of glass.
Step 1: Find the area of the window
Rectangular part is The semicircular is
The total amount of glass is
Step 2: Solve for x x
the length can not be
negative so the
window is 34x68 2x

5. Your turn
The length of the sides of a rectangular
window have the ratio 1.6 to 1. the area of
the window is sq in. What are the
window dimensions.
The shorter side is x and the other side is 1.6x
1.6(42)=67.2
42x67.2 are the dimensions
of the window

6. Solving a Perfect Square Trinomial Equation
What is the solution of
Perfect square so factor the left side
Applied square roots to both sides
Rewrite as two equations and
solve for x
Your turn
What is the solution of
Answers:2,12

7. Note: You can form a perfect square trinomial form
from by adding
When solving an equation by completing the square
Rewrite the equation in the form
To do this, get all terms with the variable on one side
of the equation and the constant in the other side.
Divide all the terms of the equation by the
coefficient of if it is not 1.
2. Complete the square by adding
3. Factor the trinomial
4. Find the square roots5. Solve for x

8. Solving by completing the square
What is the solution of
Rewrite. Get all the terms with x in one side
Divide by the coefficient of
a=1,b=-4
Find
Add 4 to both sides
Factor the trinomial
Find the square root and solve for x

9. 2. What is in vertex form? Name the vertex and y-intercept.
Your turn
1. What is the solution of
Answers:
2. What is in vertex form? Name the vertex and y-intercept.
Add to complete
the square. Also subtract
to leave the function unchanged
Factor the perfect
square, simplify
Vertex:(-2,-10) the y-int. is (0,-6)

10. Note:
You can solve a quadratic equation
In more than one way. In general, you can find a
Formula that gives values of x in terms of a,b,c
The discriminants and the solutions of quadratic equations
If > 0 two real solutions. Two x-intercepts
If =0 one real solution. One x-intercept
If <0 no real solutions. No x-intercepts

11. Answer: The least amount you can charge for a CD is $15.29 to make a
Your turn
Your school’s jazz band is selling CDs as a
fundraiser. The total profit P depends on
the amount x that your band charges for
each CD. The equation
models the profit of the fundraiser. What is the least amount,
in dollars, you can charge for a CD to make a profit of $200
a= -1
b= 48
c=-500 the write
the Q.F. and
substitute
Answer: The least amount you can charge
for a CD is $15.29 to make a
profit of $200

12. Now that you know a,b,c use the D.F.
Your turn again
You hit a golf ball into the air from a height
of 1 inch above the ground with the initial velocity of 85 ft/sec.The function
models the height, in feet of the ball at time t , in seconds. Will the ball reach a height of 115 ft?
Now that you know a,b,c use the D.F.
The discriminant is negative
so the equation
Has no real solutions.The golf ball
will NOT reach 115 ft

13. Classwork odd Homework even
Pg exercises 12-75
Pg exercises 11-55