Name: Date: 2.5 Assignment: Analyzing Functions, Data, and Quadratics Instructions Answer the five questions provided below. Answers can either be typed or handwritten. Be sure to write neatly and format all calculations correctly. If you choose to type your answers directly in the Word document, please use the Insert -> Equation tool. You may submit using any of the following formats: Word document . A photo of the Word document A photo of your answers on a separate piece of paper. In this case, you do not need to copy each question, but be sure to number your answers clearly. ended. Uncan use a atil vol. and with the equation v - - estion, you will create this lin - Questions Toni has started training for an upcoming bicycle race and has been keeping track of her practice rides. The data she's collected is listed in the table below. Distance (miles) Time (mins) 4.3 7.8 3 12.2 15.7 20.5 A) Use the graphing tool at https://www.desmos.com/calculator to plot the data points given in the table. Post a screenshot of your graph below. Report 315 AMXS FOUO) which must be protected ed disclosure or misuse of this PEQuestion 1 cont. woled ilgmis ent waiver B) Notice that the points are very close to being in a straight line. This means that we can use a linear equation to represent the data. For this part of the question, you will create this linear equation. On your desmos graph, start with the equation y = x and try different coefficients for x until you get an equation that matches up to the data points. NOTE: The data points do not all have to fall on the line; however, they should all be close to the line. State your linear equation: Post a screenshot of your graph below. Make sure that your linear equation is visible in the screenshot. C) Since the linear equation is a good representation for Toni's bike rides, we can use it to help predict the time it will take Toni to ride distances which are not listed in the chart. Use the linear equation in your graph to give an estimate for how much time Toni should allot for a 6- mile ride. Explain how you got your answer. State the approximate time it will take Toni to ride 6 miles: Explanation for how you got your answer:2. Review the graph below. - 5 -4 -3 -2 -1 0 2 3 4 5 A) Does the Vertical Line Test pass at x = -1? Explain your answer. B) Does the Vertical Line Test pass at x = 3? Explain your answer. C) Based on your results in Part A and Part B, does the graph represent a function? Why or why not? mation herein acy Act of 1973. Attempt to use the ac-Method to factor the following expressions. . Expression 1: 2x2 - x - 28 Expression 2: 2x2 + 3x + 5 A) Provide calculations for Expression 1 here: nolessiqxe sniwollot on tojest of beau ed tonnes slumof Isimonty coupe joshad a vew plelover 08 + wol 4 w B) Provide calculations for Expression 2 here: C) Explain what you observed about using the ac-Method to factor these two expressions.4. The following formulas are known as perfect square trinomial formulas. a2 + 2ab + 62 = (a + b)2 a2 - 2ab + 62 = (a - b) 2 Explain why a perfect square trinomial formula cannot be used to factor the following expression. w2 + 16w + 36Consider the quadratic expression and its factored form below. x2 - 12x + 35 = (x - 7)(x-5) second term in each factor Looking at the second term in each factor, notice that when we multiply -7 and -5, the product is equal to 35, which is the same as the constant in the quadratic. Also, notice that when we add - 7 and -5, we get -12, which is the same as the coefficient of x in the quadratic. A) Explain why the product of -7 and -5 is equal to the constant. B) Explain why -7 plus -5 is equal to the coefficient of x. For Official as amended