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Quadratic equations

Quadratic equations. A review. Factorising Quadratics to solve!- four methods. 1) Common factors you must take out any common factors first x 2 +19x=0 x(x+19) = 0 x= 0,-19 2) Recognition these are called cookie cutters (a+b) 2 , (a-b) 2 or (a+b)(a-b)=0

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Quadratic equations

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  1. Quadratic equations A review

  2. Factorising Quadratics to solve!- four methods • 1) Common factors you must take out any common factors first x2+19x=0 • x(x+19) = 0 x= 0,-19 • 2) Recognition these are called cookie cutters (a+b)2, (a-b)2 or (a+b)(a-b)=0 Proof to perfect square • Proof to difference of two squares • 3) Cross method • 4) Quadratic formula

  3. A warm up activity- solve the following • 1) x2+6x+5=0 • 2) x2-3x-40=0 • 3) X2-9=0 • 4) x2-11x=0 • 5) x2-169=0 • 6) 9x2-25=0

  4. Homework • 16th January • Ex 23, 24, Quadratic Formula 25 • Choose all or odd questions

  5. Cross Method- Factorising Quadratics • Solve x2 +15x+56 = 0 • There are three steps to follow: • Step 1 draw a cross and write the factors of 5m2 • Step 2 write down the factors of the constant 56 so that cross ways they add up to the middle term which is 15x. Remember here the sign of the constant is very important. Negative means they are different and positive means the signs are the same • Step 3 write from left to right top to bottom the factorised form.

  6. Another example using cross method • Solve : x2-3x-40 = 0 • The minus 40 tells me the factors have different signs.

  7. Yet another example of cross method • Solve x2+3x-180=0

  8. How does the cookie cutter work? • (x+2)2 = x2 + 4x + 4 • You should recognise that the right hand side is a perfect square- a cookie cutter result • There are three cookie cutter results • What are they?

  9. Perfect Square • Look at this: what is (a+b)2 =? • a b • a • b

  10. There are many ways to solve quadratic equations • Factorise any common factors first! • A) Cross method • B) Standard results cookie cutters • Now we are going to look at: • C) solving quadratics by using the quadratic formula!

  11. The Quadratic formula • Remember this:

  12. The Quadratic formula • Ok let’s prove this using the method of completing the square. • An animation deriving this • Some examples here

  13. The Quadratic Formula • Using the quadratic formula. Sometimes you cannot use the cross method because the solutions of the quadratic is not a whole number! • Example solve the following giving you solution correct to 3 sig fig • 3x2-8x+2 = 0

  14. Solving quadratic equations • Example 1 Solve x2 + 3x – 4 = 0 • Example 2 Solve 2x2 – 4x – 3 = 0 • This doesn’t work with the methods we know so we use a formula to help us solve this.

  15. Quadratic formula • Form purple math an intro • A song • Where does it come from?

  16. Example • Example Solve 2x2 – 4x – 3 = 0 • a = 2, b = -4 and c = -3

  17. Using you brain! • Only use the quadratic formula to solve an equation when you cannot factorise it by using • A) cookie cutter • B) cross method

  18. Some word problems • The height h m of a rocket above the ground after t seconds is given by h =35t -5t2. When is the rocket 50 m above the ground?

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