1. © The Visual Classroom 3.7 Standard Form of a Quadratic Relation y = a(x – s)(x – t)factored form y = ax 2 + bx + cstandard form (expanded form) Example: Expand these expressions 1. (x + 4)(x – 6) Use the distributive property = x 2 = x 2 – 2x – 24 + 4x Collect like terms – 6x– 24

2. © The Visual Classroom = (w – 5)(w – 5) 2. (w – 5) 2 Expand and simplify Use the distributive property = w 2 = w 2 – 10w + 25 – 5w Collect like terms – 5w+ 25 3. (a – 8)(a + 8) = a 2 + 8a = a 2 – 64 – 8a – 64 Collect like terms

3. © The Visual Classroom 4. (2x – 5y)(3x + 7y) = 6x 2 + 14xy = 6x 2 – xy – 35y 2 – 15xy – 35y 2 Collect like terms Expand and simplify

4. © The Visual Classroom 5. – 3(m – 2n)(m + 8n) = – 3m 2 – 18mn + 48n 2 Multiply the brackets, then multiply by – 3 Expand and simplify = – 3[(m – 2n)(m + 8n)] = – 3[ m 2 + 8mn – 2mn – 16n 2 ] = – 3[ m 2 + 6mn – 16n 2 ]

5. © The Visual Classroom Determine the missing information. a) x 2 – 2x – 15 = (x – 5)( ? ? ) = (x – 5)(x + 3) = (2x + 5)(3x – 4) b) 6x 2 + 7x – 20 = (2x + 5)( ? ? )

6. © The Visual Classroom Determine the expanded form of the equation of the parabola. y = a(x – s)(x – t) y = a(x + 1)(x – 3) 4 = a(1 + 1)(1 – 3) 4 = a(2)(– 2) 4 = a(– 4) – 1 = a y = – (x + 1)(x – 3)

7. © The Visual Classroom y = – (x + 1)(x – 3) y = – [(x + 1)(x – 3)] y = – [x 2 – 3x + x – 3)] y = – [x 2 – 2x – 3)] y = – x 2 + 2x + 3

8. © The Visual Classroom Write an expression for the area. 2a + 5 A = (2a + 5) 2 = (2a + 5)(2a + 5) = 4a 2 + 10a = 4a 2 + 20a + 25 + 10a + 25

9. © The Visual Classroom A stone is dropped from a bridge that is 20 m above a river below. The table gives the height of the stone as it falls. Time00.511.52 Height20.00018.77515.1008.9750.400 a) Create a scatter plot and draw a graph of best fit. b) Find the approximate time when the stone hits the water. c) Use (0, 20) as the vertex and indicate the other zero. d) Determine an algebraic expression, in standard form, that models the data. e) Use a graphing calculator to determine the quadratic regression equation for the data. Page 300 # 12

10. © The Visual Classroom b) Approximate time the stone hits the water is 2.1 sec. time (sec) height (m) c) The other zero would be (-2.1, 0). d) y = a(x – s)(x – t) y = a(x – 2.1)(x + 2.1) 20 = a(0 – 2.1)(0 + 2.1) 20 = a (– 4.41) – 4.535 = a y = – 4.535 (x – 2.1)(x + 2.1)

11. © The Visual Classroom y = – 4.535 (x – 2.1)(x + 2.1) y = – 4.535(x 2 – 2.1x + 2.1x – 4.41) y = – 4.535(x 2 – 4.41) y = – 4.535x 2 + 20