warm up. solving quadratic equations by the quadratic formula
TRANSCRIPT
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.