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 2am

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 2a

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Example 1:3x2 – 9x + 1 = 0

Ex 2: 2x2 = 4 – 7x 2x2 + 7x – 4 = 0

Ex 3: Solve: 3x2 – 4x - 2 = 0

Ex :4 Solve: x2 - 4x - 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

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

Discriminant of a Quadratic 3 possibilities b²-4ac 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? 3x2 – 5x + 1 = 0 “discriminate” Negative: no solution Zero: one solution Positive: two solutions 2 solutions

Ex 6: How many solutions? y = x2 – 3x + 7 = 0 “discriminate” Negative: no solution Zero: one solution Positive: two solutions 0 solutions

Ex: 7How many solutions? f(x) = x2 – 12x + 36 = 0 “discriminate” Negative: no solution Zero: one solution Positive: two solutions 1 solutions

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