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Worksheet on Linear and Quadratic Functions February 2, 2009 Linear Functions 1. Find an equation of the line through (4,5) which is perpendicular to the line 7x + 6y = -3. 2. Find an equation of the line through (1,4) which is parallel to the line -4x + 6y = 2. 3. Find an equation of the line with the same x intercept as the line 2x – 9y = 14 and the same slope as the line x – y = 21. 4. If f is a linear function such that f(4) = 7 and f(7) = 16, find the equation for f(x). 5. Find an equation of the perpendicular bisector of the line segment joining (4,-3) and (8,5). 6. Find the equation of the tangent line to x + y = 169 at (-5,12). 7. Find the equation of the line which has x intercept 5 and which is perpendicular to 7x – 2y = 13. Graph 8. y = 3x + 1 9. 2y = x – 5 10. 6x + 5y + 14 = 0 11. -4x + y + 6 = 0 Problem solving 12. Hooke’s law states that the relationship between the stretch s of a spring and the weight w causing the stretch is linear (a principle upon which all spring scales are constructed). A 10-pound weight stretches a spring 1 inch, while with no weight the stretch of the string is zero. A. Find a linear function f: s = f(w) = mw + b that represents this relationship. [Hint: Both points (10,1) and (0,0) are on the graph of f.] B. Find f(15) and f(30) – that is, the stretch of the spring for 15-pound and 30-pound weights. C. What is the slope of the graph of f? D. Graph f for 2 2 0 w 40 . Quadratic Functions 1. Rewrite the function f(x) = 2x - 4x + 5 in the form f(x) = a(x – h) + k. 2. Find the vertex of the graph of f(x) = 9x – 12x – 1. 3. Find the maximum value of f(x) = -x + 6x + 17. 4. Find the maximum value of the product x(1-x). 5. Given that f is a quadratic function with min f(x) = f(2) = 4, find the axis, vertex, range, and x intercepts. Graph, find the axis, vertex, domain and range. intervals over which f is increasing, and intervals over which f is decreasing. 6. f(x) = x + 6x + 11 7. f(x) = -x + 6x – 6 8. ½ x + 2x + 3 Problem solving 9. A rectangular dog pen is to be made with 100 feet of fence wire. A. If x represents the width of the pen, express its area A(x) in terms of x. B. Considering the physical limitations, what is the domain of the function A? C. Graph the function for this domain. D. Determine the dimensions of the rectangle that will make the area maximum. 10. A 400-room hotel in Las Vegas is filled to capacity every night at $70 a room. For each $1 increase in rent, four fewer rooms are rented. If each rented room cost $10 to service per day, how much should the management charge for each room to maximize profit? What is the minimum profit? 2 2 2 2 2 2 2

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posted: | 11/22/2009 |

language: | English |

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