The Quadratic Formula for solving equations in the formax2 + bx + c = 0
Sing to the tune of “Pop Goes the Weasel”x is equal to negative bplus or minus the square rootof b squared minus 4acALL 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
314
322 x
2
322
Example:
2m2 − 7m − 13 = −10
2m2 − 7m − 3 = 0
a=2, b = -7, c = -3
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)2(2)3(*)2(4)7()7( 2
m
m
m
SOLUTION REAL NO2
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)1(2)8(*)1(4)3()3( 2
k
k
x
Example:
k2 + 8 = 3k
k2 -3k + 8 = 0
a= , b = , c =
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 ( ).
Put in standard form by subtracting 3k from both sides.
SOLVING POLYNOMIAL EQUATIONS (2 SOLUTIONS):Put Equation in standard form, ax2 + bx + c = 0.3 methods:
1)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) = 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
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:Example
2
2
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x
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solution real No ,Impossible3
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:Example
2
2
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x
Which method would you use to solve each equation. Explain why and state the solution. Method Why? Solution7.
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11. Memorize the quadratic formula! Use the song!
