1. Lessons 9.2-9.3 The quadratic Formula and the discriminant
Algebra 2 Honors

2. Ways to solve Quadratic equations
Factoring
Square root method
Completing the square
Quadratic Formula (today!)

3. Quadratic Formula
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4. Using the quadratic formula to solve
Set equation equal to zero and define a, b, and c
Plug into the formula
Solve for the discriminant
Simplify the radical
Split into two solutions
Check your answer
2𝑥 2 −3𝑥=−5

5. The discriminant
𝑏 2 −4𝑎𝑐

6. 𝑥 2 +5𝑥−6=0 2𝑥 2 −7𝑥−15=0 𝑥 2 −8𝑥+16=0 2𝑥 2 +9𝑥+20=0
Without solving the quadratic equation, state the number and nature of the solutions.
𝑥 2 +5𝑥−6=0
2𝑥 2 −7𝑥−15=0
𝑥 2 −8𝑥+16=0
2𝑥 2 +9𝑥+20=0
Solutions:
Discriminant = 49
two rational roots
b) Discriminant = 169
c) Discriminant = 0
One rational (double root)
d) Discriminant = -79
Two imaginary solutions

7. Solve using completing the square and quadratic formula
2𝑥 2 −5𝑥+3=0
Which method did you prefer and why?