Presentation on theme: "The Quadratic Formula for solving equations in the form"— Presentation transcript:
1 The Quadratic Formula for solving equations in the form ax2 + bx + c = 0Sing to the tune of “Pop Goes the Weasel”x is equal to negative bplus or minus the square rootof b squared minus 4acALL over 2aUse 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 is2
2 Example:2m2 − 7m − 13 = −102m2 − 7m − 3 = 0a=2, b = -7, c = -3Put 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 = 3kk2 -3k + 8 = 0a= , b = , c =Put in standard form by subtracting 3k from both sides.
5 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 = 3Standard form: x2 – 2x - 3 = 0.Factored: (x+1)(x-3) = 0So 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 Formulaif ax 2 + bx + c = 0 , then
7 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? Solution220.127.116.11.11. Memorize the quadratic formula! Use the song!