Question

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 to flip it and make the hills steeper. Then, I added 3 to shift it to the right. F(x) =– (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–)(x – 5)

Answer 1

See attachment for graphs

1) Error: 3 zeros (x-intercepts) does not make 3 peaks (vertices)

2) Errors: Multiplying it by a negative is a reflection (not a steeper slope). Adding 3 on the outside of the factors is a vertical shift up (not a horizontal shift to the right).

3) Error: Multiplying by 4 makes a steeper slope (not a shallow slope).