The area of a circle varies directly as the square of the radius. = kr2 1k = p2 Pressure of a gas varies inversely as volume. P = k V The area of a triangle varies jointly as its base and its height. = kbh Ak = 1 2B Direct Variation y varies directly as the nth power of x if for all x there exists a nonzero real number k such that y =kxn. Inverse Variation y varies inversely as the nth power of x if for all x there exists a nonzero real number k such that y = k xn . Joint Variation Let m and n be real numbers. Then y varies jointly as the nth power of x and the mth power of z if for all x and z there exists a nonzero real number k such that y =kxnzm. Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. 1. ƒ1x2 = 31x + 422 - 5 2. ƒ1x2 = - 2 3 1x - 622 + 7 3. ƒ1x2 = -3x2 - 12x - 1 4. ƒ1x2 = 4x2 - 4x + 3 (Modeling) Solve each problem. 5. Area of a Rectangle Use a quadratic function to find the dimensions of the rectangular region of maximum area that can be enclosed with 180 m of fencing, if no fencing is needed along one side of the region. 6. Height of a Projectile A projectile is fired vertically upward, and its height s1t2 in feet after t seconds is given by the function s1t2 = -16t2 + 800t + 600. (a) From what height was the projectile fired? (b) After how many seconds will it reach its maximum height? (c) What is the maximum height it will reach? (d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground? (e) After how many seconds, to the nearest tenth, will the projectile hit the ground? Chapter 3 Review Exercises 425 CHAPTER 3 Review Exercises 3.7 Variation Concepts Examples
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