Section 3.6 (Sullivan, 8th ed.) MAC1140, MAC11473-6: Mathematical Models: Constructing FunctionsFor any quadratic equation f(x) = ax2 + bx + c, it will have its minimum or maximum at its vertex. It will be a maximum if a < 0 because the parabola will open downward; it will be a minimum if a > 0. The vertex can be found without graphing: Vertex =  FHGIKJFHGIKJbafba2 2,. Axis of symmetry: the line x =  ba2.1. Volume of a Cylinder: If the volume of a cylinder is V = r2h and the height is half the radius, express the volume V as a function of r.3. Finding the area of a rectangular field with fixed perimeter:George has 2000 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.a) Express the area A of the rectangle as a function of x, where x is the length:b) What is the largest area?3. A rectangle has one corner on the graph of y = 36 - x2, x > 0, at (x, y); another at the origin; and a third on the positive x-axis at (x, 0), and a fourth on the positive y-axis. Express the area A of the rectangle as a function of x. Find the area of a triangle with vertex (3, 0).4. Let P = (x, y) be a point on the graph y = x2 + 3.a. Express the distance d from P to the origin b. Find the distance if x = 0as a function of x.c. Find the distance if x = -3Section 3.6 (Sullivan, 8th ed.) MAC1140, MAC11475. A rectangle is inscribed in a circle of radius 7 with its center at the origin. Let P = (x, y)be the point in quadrant I that is a vertex of vertex of the rectangle and on the circle.a. Express the area of the rectangle as a function of x. b. Express the perimeter of the rectangle as a function of x.6. An island is 6 miles from point P, and P is 20 miles from the nearest town on a straight shoreline. a. If a person can row an average speed of 5 miles/hour and walk an average speed of 6 miles an hour, express the time T that it takes to go from the island to the town as a function of the distance x from P to where the person lands the boat.b. What is the domain of x?c. How long will it take to travel to town from the island if the boat lands 7 miles from P?Section 3.6 (Sullivan, 8th ed.) MAC1140, MAC1147Pg. 280:2. Volume of a cone: V = 1/3r2h. If height is twice the radius, express the volume V as a function of r.6. Demand Equation: x = -20p + 500, 0 ≤ p ≤ 25a. Express revenue as a function of x.b. What is the revenue if 20 units are sold.d. What quantity x maximizes revenue? What is the maximum revenue? e. What price should the company charge to maximize its revenue? 8. Enclosing a rectangular field: Beth has 3000 feet of fencing available to enclose a rectangular field. One side lies along a river, so only three sides require fencing.a. Find the area A of the rectangle as a function of x, where x is the length of the side parallel to the river.b. Find the maximum area that can be enclosed. 14. A right triangle has one vertex on the graph of y = 9 – x2, x 0, at (x, y); another at the origin; and a third on the positive x-axis at (x, 0). Express the area A of the triangle as afunction of x. 18. A circle of radius r is inscribed in a square.a. Express the area A of the square as a function of radius r of the circle.b. Express the perimeter p of the square as a function of