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Sketching Graphs of Quadratic Functions In Exercises 9-12, sketch the graph of each quadratic function and compare it with the graph of
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Chapter 3 Solutions
EBK COLLEGE ALGEBRA
- Sketching Graphs of Quadratic Functions In Exercises 9-12, sketch the graph of each quadratic function and compare it with the graph of y=x2. (a)fx=x2+1(b)gx=x21(c)kx=x2+3(d)kx=x23arrow_forwardIn Exercises 27-34, use a graphing utility to graph the quadratic function. Identify the vertex, axis of symmetry, and x-intercept(s). Then check your results algebraically by writing the quadratic function in standard form. f(x)=x2+10x+14arrow_forwardTraffic Accidents The following table shows the cost C of traffic accidents. in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s 20 25 30 35 40 45 50 Cost C 1.3 0.4 0.1 0.3 0.9 2.2 5.8 The rate of vehicular involvement in traffic accidents per vehicle-mile can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear function of s, so we expect that C the product of these two functions can be modeled as a cubic function of s. a. Use regression to find a cubic model for the data. Keep two decimal places for the regression parameters written in scientific notation. b. Calculate C(42) and explain what your answer means in practical terms. c. At what speed is the cost of traffic accidents for commercial vehicles driving at night on urban streets at a minimum? Consider speeds between 20 and 50 miles per hour.arrow_forward
- Fill in the blanks. When the graph of a quadratic function opens downward, its leading coefficient is and the vertex of the graph is a .arrow_forwardHeight of a basketball The path of a basketball thrown from the free throw line can be modeled by the quadratic function f(x)=0.06x2+1.5x+6, where x is the horizontal distance in feet from the free throw line and f(x) is the height in feet of the ball. Find the maximum height of the basketball.arrow_forwardIn Exercises 9-14, match the polynomial function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] f(x)=2x25xarrow_forward
- In Exercises 57-62, find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts (There are many correct answers.) (5,0),(5,0)arrow_forwardIn Exercises 13-26, write the quadratic function in standard form and sketch its graph. Identify the vertex, axis of symmetry, and x-intercept(s). g(x)=x28xarrow_forwardIn Exercises 5-8, match the quadratic function with its graph. [ Thegraphsarelabeled(a),(b),(c),and(d). ] f(x)=x22arrow_forward
- Describe the connections between Write the vertex form of a quadratic function, f(x) = a(x – h)? + k, and the transformation form, glx) = A · f(x – C) + D, of the basic quadratic function, y = f(x). %3Darrow_forwardSOLVE STEP BY STEP IN DIGITAL FORMAT In exercises I to VI, use the graph of to match the function with its graph. ++ 6 3 2 -6-5-4-3-2-1 -2 دارد 1. y = f(x + 5) II. y = -f(-x) - 2 III. y = f(x+6) + 2 -3 + ( ( ( + 12345 b ) ) ) 8 f(x) 7 9 10 a X ( ) IV. y = f(x) - 5 V. y = -f(x-4) ( ) VI. y = f(x-1) + 3 ( )arrow_forwardThe purpose of this analysis is to model available atmospheric carbon dioxide data with a quadratic function of the form f(x) = ax2 + bx + x. In the space below, type the model quadratic function for the relationship between year and mean carbon dioxide levels in standard mathematical form using the coefficients calculated on the spreadsheet. Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2030. Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2050. What other factors might need to be taken into account to provide a more robust model to make predictions regarding future atmospheric carbon dioxide levels?arrow_forward
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