1. Quadratic Equations Chapter 10
OBJECTVES
Find x-intercepts by factoring
Find x-intercepts by extracting square roots
Find x-intercepts by completing the square
Find x-intercepts using the quadratic formula

2. Quadratic equation in x – an equation that can be written in the general form
ax2 + bx + c = 0
where a, b, and c, are real numbers .
A quadratic equation is also known as a second-degree polynomial equation in x, p. 110.

3. Solve 2x2 = 19x + 33 for x by factoring.
1. Set equation equal to zero, called general form.
2x2 – 19x – 33 = 0
2. Express as a product of linear factors, called factoring
2x2 – 19x – 33 = 0 3
-11
( 2x ) ( x ) = 0

4. 3. Set each linear factor equal to zero and solve for x
( 2x + 3 ) ( x – 11 ) = 0
2x + 3 = 0 , x – 11 = 0
x = – 3/2 , x = 11
We used the Zero Factor Property
If ab = 0 , then a = 0 or b = 0.
F O I L
2x2 – 22x + 3x– 33 = 0
2x2 – 19x – 33 = 0
Check:
( 2x + 3 ) ( x – 11 ) = 0

5. Solve 2x2 + 3x – 5 = 0 for x by factoring.
– 1
( 2x ) ( x ) = 0
2x + 5 = 0 , x – 1 = 0
2x = – 5 , x = 1
x = – 5/2 , x = 1

6. Area using quadratics
The floor of a one-story building is 14 feet longer than it is wide. The building has 1632 square feet of floor space.
w + 14
width = w
length = w + 14
Area = 1632 w
VERBAL
MODEL:
Length =
Width
Area
ALGEBRAIC lw = A
MODEL:

7. ALGEBRAIC lw = A
MODEL:
( w + 14 ) w = 1632
w2 + 14w = 1632
w w – 1632 = 0
( w – 34 ) ( w + 48 ) = 0
w – 34 = 0 , w = 0
w = 34 , w = -48
Therefore, the width is 34 and the length is 48.

8. Extracting Square Roots
The equation u2 = d, where d > 0, has exactly two solutions:
and
These solutions can also be written as

9. Solve the equation x2 = 32 by extracting the square roots.
EXACT ANSWER !!
List both the exact solution and the decimal solution rounded to two decimal places. or

10. Solve the equation ( x + 13 ) 2 = 25 by extracting the square roots.
x = or x =
x = -8 or x = -18
Try p. 120 # 21-34

11. The Empire State building is 1453 feet tall.
Position equation- an equation that gives the height of an object that is falling, s = -16t2 + v0t + s0 s = height of the object (above ground) v0 = initial velocity s0 = initial height of object t = time
The Empire State building is 1453 feet tall.
Suppose an object falls from rest the position equation is
s = -16t2 + (0)t or
s = -16t

12. Suppose King Kong falls from the top of the empire state building.
a) Use the position equation to write a mathematical model for the height of King Kong.
s = -16t
b) Find the height of King Kong after 4 seconds.
s = -16(4)
s = -16(16)
s =
s = 1197

13. c) How long will it take before Kong hits the ground.
or approximately 10 seconds

14. Solve the quadratic equation x2 + 8x + 14 = 0 by completing the square.

15. Consider again 2x2 +3x – 5 = 0 with solutions x = – 5/2 , x = 1
Consider again 2x2 +3x – 5 = 0 with solutions x = – 5/2 , x = 1 . Solve the equation by completing the square.
2x2 +3x = 5
1(2x2 +3x = 5) 2

16. x = 4/4 or x = -10/4,

17. Completing the Square To complete the square for the expression add , which is the square of half the coefficient of x. Consequently,
The Quadratic Formula
The solutions of a quadratic equation in the general form
are given by the Quadratic Formula

18. Consider again 2x2 +3x – 5 = 0 with solutions. x = – 5/2 , x = 1
Consider again 2x2 +3x – 5 = 0 with solutions x = – 5/2 , x = 1 . Solve the equation by using the quadratic formula.
2x2 +3x – 5 = 0
a = 2, b = 3 , c = – 5
x = 4/4 or x = -10/4
x = 1 or x = -5/2

19. The solutions of a quadratic equation
can be classified as follows.
If the discriminant b2 – 4ac is
1. positive, the equation has two distinct real solutions and its graph has two x-intercepts.
2. zero, the equations has one repeated real solution and its graph has one x-intercept.
3. negative, the equation has no real solution and its graph has no x-intercept.

20. Homework
Homework: p. 574 # 1- 47,
P. 579 # 1-30
Read Chapter 10.1 – Key Concepts
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