Math 141 - Algebra with Applications Name :. Latifa Osman Graded Class Activity 10B: Modeling with Quadratics & Factoring Sections Chapter 8 **Show all work for full credit and box in your final answers. * * The speed, S, of a car determines the miles, m, per gallon that a specific car gets is shown in the table below. input Speed (mph) 20 25 30 40 50 55 50 65 70 ( 45, 30, 2 ) Output K Mileage (mpg) 25.5 27.5 29 30.0 30.2 29.5 28.8 27.4 25.3 y = a ( x - h ) 2 + k Create a scatter plot of the data. a. Identify the independent variable. y = a ( x - 45 ) 2 + 30. 2 b. Identify the dependent variable. ( x , y ) = (70 , 25 . 3 ) c. Use shifting and/or scaling of f(x) = x to find a model that closely fits the scatter plot of the given data. Write the expression as a quadratic function f (x). - 4.9 = 625 9 (70 - 45 ) + 30. 2 253 = 625a +30. 2 9 = - 0. 00784 625 625 - 30 . 2 - 30 .2 plug in d. Clearly explain the effect of each value that you used for the shifting and/or scaling of the quadratic function. e. According to your model from part a and using algebra, estimate the mileage of the car when it travels 90 miles per hour. Round to the nearest tenth. f. According to your model from part a and using algebra, estimate when the car will get 28 miles per gallon. Round to the nearest tenth. 2. Factor completely and solve for the x-intercepts. a. x - 4x + 96 x 2 - 4x- 96 383b. 2x - 10x - 72 c. 60 - 54x - 54x d. - 42 = x * - 13x e. 81x - 121y f. 9x - x = 10 384