Section 1.4 Day 1 Quadratic Equations No Calculator After this section you should be able to: Solve quadratic equations by FACTORING

Section 1.4 Day 1 – Quadratic EquationsNo Calculator

After this section you should be able to:

• Solve quadratic equations by FACTORING

Solve the following quadratic equations:28x 4x 0

4x 2x 1 0

4x 0 2x 1 0

x 01x2

22x 12x 18 0

22 x 6x 9 0

2 x 3 x 3 0

x 3 double root

2x 4x 5 0

x 5 x 1 0

x 5 x 1

22x x 6 0

2x 3 x 2 0

3x x 22


218x 9x 1 0

Now try these four…..

25x 2x 3 0

2x 16x 28 0 230 x x 0

6x 1 3x 1 0

1 1x x6 3

5x 3 x 1 0

3x x 15

x 14 x 2 0

x 14 x 2

6 x 5 x 0

x 6 x 5


2x 642x 64 0

x 8 x 8 0

x 8 x 8

2x 132x 13 0

x 13 x 13 0

x 13 x 13

2x 64x 8

2x 13x 13

2x 1 6

x 1 6

x 1 6

2x 3 16 x 3 4

x 3 4 x 1 x 7


Now try these five:

2x 10x 75 0

2x 2x 1 4

2x 41 0 22x x 6 0

2x 4 11

x 15 x 5 0 x 15 x 5

2x 1 4 x 1 2

x 1 2 x 1 x 3

2x 41

x 41 2x 3 x 2 0

3x x 22

x 4 11

x 4 11



Homework: Pg. 119 #7-15 ODD, 21-31 ODD

After this section you should be able to:



After this section you should be able to: • Solve quadratic equations by COMPLETING THE SQUARE

• Solve quadratic equations by using the QUADRATIC FORMULA

• Determine the number of solutions by using just the DISCRIMINANT of the quadratic formula.

The Method of Completing the Square21 linear term

2

2x 4x 1 0 2x 14x

2 4 14x 4x

2x 2 3

x 2 3

x 2 3

2x 2x 4 0 2x 42x

2 4 12x x 1

2x 1 5

x 1 5

x 1 5

• Solve quadratic equations by COMPLETING THE SQUARE

The Method of Completing the Square

2x 4 8x 2x 48x

2 16x 4 16x 8

2x 4 12

x 4 12

x 4 2 3

2x x 1 0 2x x 1

2 1 14

x x 14

21 5x2 4

1 5x2 4

1 5x2 2

1 5x2 2


Now try these……2x 6x 3 0 2x 8x 1 0

2x 36x 2 3 9x 6x 9

2x 3 12

x 3 12

x 3 12

x 3 2 3

2x 18x 2 16x 1 16x 8

2x 4 15

x 4 15

x 4 15


The Quadratic Formula2The two solutions of quadrat axic equat bxion are :c 0

2 cba

b2

4a

Before we begin solving (and potentially wasting time)……

2If b 4ac 0, there are real solutiNO ons.

[cannot do until Section 1.5]

Compute the value of the discriminant 2b 4ac2If b 4ac 0, there are real solutiT O s.W on[use quadratic formula or factor]2If b 4ac 0, there is real solution (double ro )NE .O ot

[perfect square….+/- square root]

Use the value of the discriminant to determine the number ofreal solutions to each of the quadratic equations below.

2x 4x 5 0 2x 3x 4 0 23x 4x 5 0

24 4 1 5

4Zero Real Solns

23 4 1 4

7

Zero Real Solns

24 4 3 5 76

Two Real Solns

2x 15 0

20 4 1 15

60

Two Real Solns

2x 4x 4 0

24 4 1 4 0

One Real Soln

2x 7x 4 0

27 4 1 4 33

Two Real Solns


Given the quadratic equation below:A) Compute the value of the discriminant.B) Determine the number of real solutionsC) Solve the quadratic equation (if possible)

22x 7x 6 0

2A) 7 4 2 6 1

B) Two real solutions

C) 2x 3 x 2 0 3x x 22

2x x 4 0

2A) 1 4 1 4 17


1 17C)2

• Determine the number of solutions by using just the DISCRIMINANT of the quadratic formula. • Solve quadratic equations by using the QUADRATIC FORMULA


2x 3x 8 0

2A) 3 4 2 8 57

B) Zero real solutions

untilC) No

SectSolu

iontion

1.5

2x 16 0

2A) 0 4 1 16 64


C) x 4 x 4 0

x 4 x 4



2x 4x 4 0

2A) 4 4 1 4 0

B) One real solution

C) x 2 x 2 0

23x x 1 0

2A) 1 4 3 1 13


1 13C)6

x 2 (double root)


Section 1.4 day 2 – Quadratic EquationsNo Calculator

Homework:

After this section you should be able to: • Solve quadratic equations by COMPLETING THE SQUARE

• Solve quadratic equations by using the QUADRATIC FORMULA


Pg. 119 #35-39odd, 59-62all,67, 68, 74

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Section 1.4 Day 1 Quadratic Equations No Calculator After this section you should be able to: Solve quadratic equations by FACTORING