Factorise This is standard quadratic so just use the method you are happy with method:- Factorise This is standard quadratic so just use the method you are happy with From ax2 + bx + c find 2 numbers that multiply to give ac and add to give b and then split bx into 2 bits and factorise:- 12d2 + 5d 2 What 2 numbers multiply to make -24 and add to make 5 :- 8 and 3 – – 12d2 + 5d 2 = 12d2 +8d 3d -2 = 4d(3d + 2) - (3d + 2) = (4d 1) (3d + 2) – – – Completing the square. You might be asked to complete the square or the question might ask you to find the minimum value of a quadratic expression. Use completing the square to find the minimum value. ax2 + bx + c. For this exam a will always just be 1 so the quadratic will be of the form x2 + bx + c. x2 + bx + c = (x + - + c Complete the square in 6x + 7. Example: x2 – The coefficient of is halve it to give Solution: x –6, –3. Squaring ( gives so to just create you need to subtract 9 from 6x + 7 = = (x 3)2 2. x2 – – – that the minimum of the expression is when = 3, since the minimum value of (x 3)2 is Notice x –2 – 0. Be careful to give the answer the question is looking for either the minimum value, the x value – required to give the minimum or both. Solving quadratic equations. by factorising. 5x + 6 = 0 (x 3)(x 2) = 0 Example: x2  – – – 3 = 0 or 2 = 0 = 3 or = 2.   x x x x – – Note that a quadratic could have just 2 terms, but it is solved in the same way. + 8x = 0  + 8) = 0 Example: x2 x(x  = 0 or + 8 = 0  = 0 or = x x x x –8 N.B. Do not divide through by first: you will lose the root of = 0. x x - 4 = 0 (x+2)(x 2) = 0  Example: x2 -  by using the formula
Factorise This is standard quadratic so just use the method you are happy with method:- Factorise This is standard quadratic so just use the method you are happy with From ax2 + bx + c find 2 numbers that multiply to give ac and add to give b and then split bx into 2 bits and factorise:- 12d2 + 5d – 2 What 2 numbers multiply to make -24 and add to make 5 :- 8 and – 3 12d2 + 5d – 2 = 12d2 +8d – 3d -2 = 4d(3d + 2) - (3d + 2) = (4d – 1) (3d + 2) Completing the square. You might be asked to complete the square or the question might ask you to find the minimum value of a quadratic expression. Use completing the square to find the minimum value. ax2 + bx + c. For this exam a will always just be 1 so the quadratic will be of the form x2 + bx + c. x2 + bx + c = (x + - + c Example: Complete the square in x2 – 6x + 7. Solution: The coefficient of x is –6, halve it to give –3. Squaring ( gives so to just create you need to subtract 9 from x2 – 6x + 7 = = (x – 3)2 – 2. Notice that the minimum of the expression is –2 when x = 3, since the minimum value of (x – 3)2 is 0. Be careful to give the answer the question is looking for – either the minimum value, the x value required to give the minimum or both. Solving quadratic equations. by factorising. Example: x2 – 5x + 6 = 0  (x – 3)(x – 2) = 0  x – 3 = 0 or x – 2 = 0  x = 3 or x = 2. Note that a quadratic could have just 2 terms, but it is solved in the same way. Example: x2 + 8x = 0  x(x + 8) = 0  x = 0 or x + 8 = 0  x = 0 or x = –8 N.B. Do not divide through by x first: you will lose the root of x = 0. Example: x2 - 4 = 0  (x+2)(x - 2) = 0  by using the formula
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