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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_forwardFill 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_forward
- Traffic 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_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_forwardIn 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_forward
- Height 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 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_forwardApplication of Differential Calculus: Optimization Farmers use a certain plant food costing $4.00 per ounce to help them in growing oranges. It is estimated that when x ounces of the food are used on an ace of orange grove, the farmer is able to get Ln(4x+5) crates of oranges from that acre of land. If the farmer can sell the oranges at $20 per crate, how many ounces should be used per acre to maximize the orange crops net value.arrow_forward
- The graph of a quadratic function is given f(x) = -x^2+8x-7 (a) Find the coordinates of the vertex and the x and y intercepts. x-intercepts (x,y) = (smaller x-value) (x,y)= (larger x- value) y-intercept. (x,y)=arrow_forwardDescribe 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_forwardThe table shows projections for the female population of a country (in millions). Year 2016 2040 181 2050 187 Female Population 158 (a) Find a quadratic function f(x) = ax? + bx + c that gives the female population (in millions) in year x, where x0 corresponds to the year 2000. (b) Estimate the female population in the year 2035.arrow_forward
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