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Published byAbel Hill Modified over 4 years ago

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**The Quadratic Formula for solving equations in the form**

ax2 + bx + c = 0 Sing to the tune of “Pop Goes the Weasel” x is equal to negative b plus or minus the square root of b squared minus 4ac ALL over 2a Use the Quadratic Formula to solve x2 – 4x – 8 = 0. Looking at the coefficients, I see that a = 1, b = –4, and c = –8. I'll plug them into the Formula, and simplify: The solution is 2

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Example: 2m2 − 7m − 13 = −10 2m2 − 7m − 3 = 0 a=2, b = -7, c = -3 Put in standard form by adding 10 to both sides. Ben very careful! Make sure to surround each value of a, b, and c with ( ). Example: k2 + 8 = 3k k2 -3k + 8 = 0 a= , b = , c = Put in standard form by subtracting 3k from both sides.

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**SOLVING POLYNOMIAL EQUATIONS (2 SOLUTIONS):**

Put Equation in standard form, ax2 + bx + c = 0. 3 methods: SQUARE ROOT METHOD: If there is no bx term or if the equation is in the form (x+ k)2 + c = 0, then just get the constant c on one side, take ± the square root of both sides and get x by itself. Note: If c is positive, then there is no real solution. 2) FACTORING METHOD: If product ac has two factors that add up to b, then it is factorable. Factor it and use the Zero Product Rule to find the solutions. This says that if A*B=0, then A=0 or B=0. Example: x2 -2x = 3 Standard form: x2 – 2x - 3 = 0. Factored: (x+1)(x-3) = 0 So x+1 = 0, which gives x = -1, or another possible solution is x-3 = 0, which gives x = 3. 3) USE QUADRATIC FORMULA: If the equation ax2+ bx+ c =0 is not factorable, then use quadratic formula. Quadratic Formula if ax 2 + bx + c = 0 , then

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**Which method would you use to solve each equation**

Which method would you use to solve each equation. Explain why and state the solution. Method Why? Solution 7. 8. 9. 10. 11. Memorize the quadratic formula! Use the song!

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