Quadratic Formula

What is the quadratic formula? 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

Does that look complicated? 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

It’s not!!!!!!!!!!!!

Example: 𝒙 𝟐 +𝟔𝒙−𝟕=𝟎 We can factor this and get: 𝑥+7 𝑥−1 =0 We can then solve and get: 𝑥=−7,𝑥=1

Solving using quadratic formula: 𝒙 𝟐 +𝟔𝒙−𝟕=𝟎 Use this: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

Solving using quadratic formula: 𝒙 𝟐 +𝟔𝒙−𝟕=𝟎 Get this: 𝑥= −6± 6 2 −4∗1∗−7 2∗1

𝑥= −6± 6 2 −4(1)(−7) 2(1) 𝑥=−7 𝑎𝑛𝑑 𝑥=1

Remember: Don’t forget to find the PLUS and MINUS versions of the answer. You will often have 2 solutions!

𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 Use quadratic formula: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 Another example: 𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 Use quadratic formula: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

Identify A, B, C: 𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 A= B= C=

𝑥= −7± 7 2 −4(2)(6) 2(2)

Odd looking answers 𝒙 𝟐 −𝟓𝒙+𝟐

Odd looking answers 𝒙 𝟐 −𝟓𝒙+𝟐 𝒙= −(−𝟓)± (−𝟓) 𝟐 −𝟒∗𝟏∗𝟐 𝟐∗𝟏

𝑥= 5+ 17 2 𝑥= 5− 17 2

Odd looking answer (2): 𝟐 𝒙 𝟐 +𝟑𝒙+𝟓

𝟐 𝒙 𝟐 +𝟑𝒙+𝟓 𝒙= −𝟑± 𝟑 𝟐 −𝟒∗𝟐∗𝟓 𝟐∗𝟐

No solution!!!!!

𝟐 𝒙 𝟐 +𝟑𝒙+𝟓