Warm Up

𝐹𝑜𝑖𝑙(𝑥+3)(2 𝑥+2)

Solving Quadratic Equations by the

Quadratic Formula

Refresh

• Remember the GENERAL FORM of a quadratic equation is

Where a,b and c are numbers.

Practice

• Write in general form and identify a,b and c.

• We need to add 3 to both sides

• a= 1 b= -5 c= 3

You try

• Answer:

• a=3 b= -4 c=5

Try again: put in general form

• Answer:

• a=1 b=0 c= -10

What does it mean to “solve”?

• When you are asked to “solve” a quadratic, it is asking you to find the roots.

THE QUADRATIC FORMULA

2 4

2

b b acx

a

What do we do with it?

Step 1: Put in General form, and set equation = to 0.

Step 2: Identify a, b, and c in your quadratic .

Step 3: Substitute a.b and c into the quadratic formula.

Example

• a=1. b=4. c=3

Example 1 continued

• x=-1 and x=-3

WHY USE THE QUADRATIC FORMULA?

The quadratic formula allows you to

solve ANY quadratic equation, even

if you cannot factor it.

Example 2

𝑥2+2𝑥=63Answer:

Example 3: You try

𝑥2+8 𝑥−84

• Answer: 6 , -14

Example 4: you try again!

• Answer: -3, 8

𝑥2−5 𝑥=24

You try! Start with 1 and 4,

then go on to the others.

2

2

2

2

2

1. 2 63 0

2. 8 84 0

3. 5 24 0

4. 7 13 0

5. 3 5 6 0

x x

x x

x x

x x

x x

1. 9,7

2.(6, 14)

3. 3,8

7 34.

2

5 475.

6

i

i

Homework:

• 9.7• 1: all• 3: a and b.