13 4 The Quadratic Formula and Discriminant Quadratic

13. 4 The Quadratic Formula and Discriminant

Quadratic Formula The boy with the negative attitude couldn’t decide whether to go to the radical party or b² and miss out on the 4 awesome chicks the party is over at 2 am

Quadratic Song to Pop Goes the Weasel x equals negative b Plus or minus the square root Of b squared minus four a c All over 2 a

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Example 1: 3 x 2 – 9 x + 1 = 0

2 2 x Ex 2: = 4 – 7 x 2 x 2 + 7 x – 4 = 0

Ex 3: Solve: 2 3 x – 4 x - 2 = 0

Ex : 4 Solve: 2 x - 4 x - 7 = 0

Special Case: 3 -x(x-3)=4 • Need to put it in standard form • Then put it in the quadratic equation a= 1, b=-3, c=1

Discriminant Determines the number of real-number solutions of a quadratic equation b² - 4 ac = discriminant

Discriminant of a Quadratic 3 possibilities b²-4 ac 1. ) If positive then 2 solutions for x 2. ) If 0 then 1 solution for x 3. ) If negative then no real solutions for x

Ex 5: How many solutions? 2 3 x – 5 x + 1 = 0 “discriminate” 2 solutions Negative: no solution Zero: one solution Positive: two solutions

Ex 6: How many solutions? 2 y = x – 3 x + 7 = 0 “discriminate” 0 solutions Negative: no solution Zero: one solution Positive: two solutions

Ex: 7 How many solutions? 2 f(x) = x – 12 x + 36 = 0 “discriminate” Negative: no solution 1 solutions Zero: one solution Positive: two solutions

Assignment: Page 593 # 2 -28, 42 -62 finding the roots is the same as solving for x