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The Quadratic Formula for solving equations in the form ax 2 + bx + c = 0

The Quadratic Formula for solving equations in the form ax 2 + 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 x 2 – 4 x – 8 = 0.

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The Quadratic Formula for solving equations in the form ax 2 + bx + c = 0

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  1. 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

  2. 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.

  3. 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

  4. 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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