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Learn to solve quadratic equations by factorization, completing the square, and using the formula. Practice rearranging equations to find "x". Explore how factors affect quadratic curves. Worksheets included.

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  1. Starter • To make sure that you can re-arrange equations • Make “x” the subject of the formula v = ω√(a² -x²) so x= ? INTO - Foundation L4/5 MH

  2. Lesson 4-5 Quadratic equations • Objectives - To solve quadratic equations by factorisation - To solve quatratic equations by completing the square - To solve quadratic equations by formula INTO - Foundation L4/5 MH

  3. Quadratic equations • These occur naturally e.g. The length of a rectangular field is 40m greater than its width. Its area is 6000m2 Form an equation to find the length of the field INTO - Foundation L4/5 MH

  4. Quadratic equations • Usually have two solutions • Look like parabolas • Take the form • Do you know how a,b,c effect the quadratic curve ? INTO - Foundation L4/5 MH

  5. They look something like this INTO - Foundation L4/5 MH

  6. Factorising quadratics • Factorise • X2+7x+12 ( x + ) ( x+ ) • X2-2x-24 ( x+ ) (x- ) • 12X2-17x-7 factors of 12 (4,3), (6,2),(12,1) factors of 7 (7,1) ( x+ ) ( x- ) INTO - Foundation L4/5 MH

  7. Solving quadratics • Once we have factorised the quadratic we have the solution • X2+5x+6 = 0 (x+2)(x+3)=0 so x=-2 and x=-3 • These are also known as the roots of the equation • Obviously, not all quadratics factorise !! INTO - Foundation L4/5 MH

  8. Can’t factorise it • Then we complete the square OR • We use the quadratic formula • Completing the square implies that the form of Is written as INTO - Foundation L4/5 MH

  9. Complete the square and solve 8x2 + 64x – 40 Step 1 divide by a Step 2 write Step 3 subtract the squared term INTO - Foundation L4/5 MH

  10. To solve • Rearrange the equation • Take the square roots of both sides • Rearrange for x INTO - Foundation L4/5 MH

  11. Derive the Quadratic formula INTO - Foundation L4/5 MH

  12. Derive quadratic formula INTO - Foundation L4/5 MH

  13. Worksheet • I have a worksheet to hand out • Factorise the first sets of equations • Complete the square to solve the second set of equations • Use the quadratic formula to solve the last set of equations INTO - Foundation L4/5 MH

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