Sometimes, a quadratic equation cannot be factored Example: x 2 + 7x + 3 = 0 There is not a pair of numbers that multiply to give us 3, that will also add up to 7. To help us solve this equation for x, when it cannot be factored, we will us the Quadratic Formula.

The Quadratic Formula can be used to solve for x on ANY quadratic equation ax 2 + bx + c = 0 X = -b ± b 2 – 4ac 2a

x 2 + 7x + 3 = 0 – b  b 2 – 4 a c 2a x =

THE QUADRATIC FORMULA The solutions of the quadratic equation a x 2 + b x + c = 0 are – b  b 2 – 4 a c 2a x = when a  0 and b 2 – 4 a c ≥ 0. You can read this formula as: x equals the opposite of b, plus or minus the square root of b squared minus 4 a c, all divided by 2 a.

To help you remember… Row, Row, Row Your Boat – Negative, negative, negative b – Plus or minus the square root – B squared minus four A C – All over two A Pop Goes the Weasel – X equals neg-a-tive b – Plus or minus the s-q-u-a-r-e root – B squared minus 4 – A – C – ALL over 2 A Brother John / Frère Jacques – Negative b, negative b – Plus or minus square root, plus or minus square root – B squared minus 4 a c, b squared minus 4 a c – All over 2 a, all over 2 a

4x 2 - 7x – 2 = 0

x 2 + 9x + 2 = 0

2x x + 3 = 0

2x 2 - 8x + 4= 0

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