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Name ____________________________________________ Date __________________ Review of Graphing Quadratics and Best Fit Lines/Curves Directions: Graph each quadratic. Answer the questions provided. 𝒚 = 𝟐𝒙𝟐 + 𝟒𝒙 − 𝟔 1. Does the parabola open up or down? Vertex a= b= Is the vertex a minimum point or a maximum point? Table of Values c= x Equation of Axis of Symmetry y Roots 2. Look at the graph below. Determine the roots, the vertex, and the equation of the axis of symmetry. Based on the graph, is the “a” value for the equation positive or negative? How do you know? Vertex Roots Equation of Axis of Symmetry 3. Using the equation of the line of best fit, which number is the best prediction of the output when the input is 13? Linear Regression Calculator {(-5, 9), (0, 42), (2, 31), (5, 97), (9, 143), (11, 151)} Quadratic Regression Calculator a. 127 b. 159 c. 170 d. 178 4. What is the curve of best fit for the scatter plot shown below? a. y = 62.15x2 + 140.32x – 9.35 b. y = -56.21x2 + 139.31x + 9.35 c. y = -1.22x + 56 d. y = 56x – 1.22 5. What is the line of best fit for the scatter plot shown to the right? a. y = -32.07x2 + 68.9x + 8.3 b. y = -3.02x + 0.01 c. y = 50.45x2 – 117.14x + 2.54 d. y = 2.1x + 0.14 6. A scientist dropped an object from a height of 200 feet. She recorded the height in 0.5second intervals. Her data is shown. Time (seconds) Height (feet) 0.0 0.5 1.0 1.5 2.0 2.5 200 195 185 165 135 100 Based on a quadratic model, what is the approximate height of the object at 3 seconds? 7. Kim and Sandy are lifeguards at the pool. They wanted to find the relation between the temperature (𝐹°) and the number of people that came swimming. The data is shown in the chart below. Temperature 78 # of People 40 Swimming 79 46 82 50 82 54 85 62 90 70 93 72 94 79 96 88 97 88 98 91 a. Describe the relationship between the temperature and the number of people swimming. How do you know it is a linear relationship? b. Use the calculator to determine the equation of the best fit line. Round to the nearest 100th. c. Using the equation, determine how many people would be swimming when the temperature is 88°. d. Using the equation, determine the temperature if 58 people are swimming. 8. The table below represents the height of a ball after it has traveled a certain distance. a. Determine the curve of best fit (quadratic regression) for the data listed in the table. Round to the nearest hundredth if necessary. b. Determine the height of the ball if it travels 30 meters. c. Determine the height of the ball if it travels 50 meters. Distance (m) Height (m) 7 8 20 15 33 24 47 26 60 24 67 21