3. Suppose f(x) is a polynomial with degree 4 and has three roots: a root at a = -3 of degree 2, a root at x = 0 of degree 1 and a root at x = 2 of degree 1. If f(-4) = 3, we aim to give a graph sketch of f(x). (a) Determine the sign decomposition of f (x): (b) Graph f(x): 3 2 (c) Find a polynomial with the same properties as f (x).1. The volume of a cone with radius, r, and height, h, is Trz h and its curved surface (or side ) area is arvr2 + h2. Suppose that the volume of a cone is 2 cubic inches. Write its curved surface area as a function of its radius.Problem 2 A rectangle is inscribed in a circle with diameter 12. Here's a picture to help you visualize: (a) Write y as a function of x. (b) Write the perimeter of the rectangle, P, as a function of the width, x. (c) Express the area of the rectangle, A, as function of the width, x.Problem 3 A triangle is bounded by the r axis and the graph of y = va. Here's a picture to help you visualize: (a) Write y as a function of x. y (b) Express the area of the triangle, A, as a function of the width, x. (c) Write the hypotenuse of the triangle, H, as a function of the width, x. (d) Write the perimeter of the triangle, P, as a function of the width, x. Problem 4 A ball is thrown in the air. Its height in feet after t seconds is given by h(t) = -16tz + 32t. (a) Write h(t) in standard form: a(t - h) + k. (b) At what time is the ball at its highest point, and how high is the ball at that time