 # Review How do we solve quadratic equations? 1.) Factoring using “Bottoms Up” 2.) if its not factorable by “Completing the Square”

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Review How do we solve quadratic equations? 1.) Factoring using “Bottoms Up” 2.) if its not factorable by “Completing the Square”

Quadratic Equations (2x 2 + 7x +5 = 0) Variable to the second power Graph is a parabola Solve by factoring if possible

Quadratic Equations (x 2 + 10x +5 = 0) Variable to the second power Graph is a parabola Solve by factoring if possible If not factorable, use “complete the square” method +25

13.4 The Quadratic Formula Objective: 1.)To use the quadratic formula to solve quadratic equations 2.) To use the discriminant to find the number of solutions for a quadratic equation

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

Quadratic Formula ( 3 x 2 –7 x + 2 = 0) 3 -7 2 3 a bc

3x 2 – 9x + 1 = 0

2x 2 – 5x - 6 = 0

2x 2 = 4 – 7x 2x 2 + 7x – 4 = 0

3x 2 – 8 = 10x 3x 2 - 10x – 8 = 0

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 the discriminant is positive then the quadratic equations has 2 solutions for x 2.) If the discriminant is 0 then the quadratic has 1 solution for x 3.) If the discriminant is negative then there are no real solutions for x

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

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

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

Solve: 3x 2 – 4x - 2 = 0

Solve: x 2 - 4x - 7 = 0

Assignment: Page 593 # 2-28, 42-52 finding the roots is the same as solving for x

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