Quadratic Equations using the formula using the formula

The Quadratic Formula … for the equation ax 2 +bx+c=0

x 2 - 4x – 1 = 0- 4– 11 a = b = c = -4 –1 1 ax 2 + bx + c = 0 √b 2 – 4ac = √(-4) 2 – (4 * 1 * -1) = √16 – -4 = √ = √20 Solve and sketch the curve

x 2 - 4x – 1 = 0- 4– 11 a = b = c = -4 –1 1 √b 2 – 4ac = √20 = 2 ± ½√20 x = --4 ± √20 2 x 1 = 4 ± √20 2 X = 4.24 or ½√ ½√20

x 2 - 4x – 1 = 0- 4– 11 X = 4.24 or Solve and sketch the curve sketch x y

Example problem Leaving answers as surds Solve 2x 2 + 8x +7 = 0 and sketch Does not factorise This tells you that

Example problem Leaving answers as surds Solve 2x 2 + 8x +7 = 0 x = / 2  2 Or x = / 2  2 a = 2 b = 8 c = 7 a = b = c = 7

Plenary Solve 3x 2 + 5x + 4=0 a = [coefficient of x 2 ] b = [coefficient of x] c= [constant] = 3 = 5 = 4 b 2 - 4ac = 5 2 – (4 x 3 x 4) = 25 – 48 = -23  b 2 - 4ac =  -23 Impossible --> equation has no roots (y=3x 2 + 5x+4 doesn’t cross x-axis)