Take a look at teen 1's initial polynomials for three layers of hills. Teen 1 has described what he thinks each modification to the initial polynomial will do. Sketch each curve (in a different color, preferably). (You will be asked to find and repair mistakes in the next section.) (6 points: 2 points for each curve) Hill 1: My first layer needs three peaks. I chose three points on the x-axis (the three zeros), and then I wrote each as a binomial to create the first polynomial. F(x) = (x - 1)(X - 3) (X - 4) Hill 2: My second layer should be a useful transformation of the first. Using the first polynomial as the base, I multiplied it by -(12) to flip it and make the hills steeper. Then, I added 3 to shift it to the right. F(x) =-1/2(x -1)(x - 3)(x - 4) + 3 Hill 3: This hill should be a shallow parabola that will rise up in the foreground of my picture. F(x) = 4(X-1/2)(x - 5)