5.4 The Quadratic Formula MATHPOWERTM 10, Ontario Edition, pp. 288-295 To solve a quadratic equation using the quadratic formula, write the equation in the form ax2 + bx + c= 0, a*0. The quadratic formula is x = --btvb2 - 4ac 2a 1. Solve using the quadratic formula. 4. Application Use the Pythagorean Theorem a) x2 - 8x + 12 =0 b) 212 -3y -2=0 to find the value of y, to the nearest hundredth. 1 + 2 c) 20x2 + 27x = 14 d) 48x2- 58x + 15 = 0 Problem Solving 5. The sum of the squares of three consecutive 2. Solve using the quadratic formula. Express odd integers is 875. Find the integers. answers as exact roots. a) x2 - 6x + 3 =0 b) 3x2 + 5x + 1 =0 6. A plain mat is placed around a picture measuring 28 cm by 36 cm so that the width of c) 3x2- 6x-8=0 d) 4x(x + 8) =3 the mat is equal on all sides. The area of the mat is - of the area of the picture. Find the width of the mat, to the nearest millimetre. e ) b2 +. 36 = 1 f) 4x2 - 2x +5=0 7. A window is in the shape of a rectangle 3. Solve using the quadratic formula. Round to surmounted by a semicircle. The height of the the nearest hundredth, if necessary. rectangle is 0.4 m more than the width. The total a) x2 + 13x + 9 =0 b) 4x2 - 11x - 19 =0 area of the window is 10.4 m?. Find the width and height of the window, to the nearest hundredth. c) 1.6(y3 + 5) = 13.4y d) 18x2 + 5x + 17 = 0 8. . Communication Is it possible to write two e) at -44 = 0 . f) ( x + 1)2 + (x+3)2= 25 real numbers whose sum is 4 and whose product is 5? Use the quadratic formula to help you explain