Lesson 5.6: The Quadratic Formula & the Discriminant

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Presentation transcript:

Lesson 5.6: The Quadratic Formula & the Discriminant The Quadratic Formula is used to solve ANY quadratic equation. 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 To use the formula: Equation must be in standard form Equation must be equal to zero Pick out a, b, & c Plug & Chug

Solve using the quadratic formula. 1) 3 𝑥 2 +8𝑥=35 2) 2 𝑥 2 +𝑥= 𝑥 2 −3𝑥−4

3) 3 𝑥 2 −6𝑥=5 4) −2 𝑥 2 =−2𝑥+3

The Discriminant is used to determine the number and type of solutions of a quadratic equation. 𝑏 2 −4𝑎𝑐=+# → 2 Real Solutions 𝑏 2 −4𝑎𝑐= 0 → 1 Real Solutions 𝑏 2 −4𝑎𝑐=−# → 2 Imaginary Solutions

Determine the number and type of solution of each quadratic equation. 5) 9 𝑥 2 +6𝑥+1=0 6) 9 𝑥 2 +6𝑥−4=0 7) 9 𝑥 2 +6𝑥+5=0

HOMEWORK: p.295 #18-62 (EOE)