Answer:
Part A) Kesley is correct
Part B) g'(x)=3x2-2x-4
Part C) Graph attached
Part D) Explained
Step-by-step explanation:
Part A)
Kelsey is correct because no. of 0s in a 3rd degree polynomial be 3. which means the no. of intercepts will be 3. Thus Ray is incorrect as no. of 0s and x-intercept are similar thing.
Further a graph is attached of g(x) = x3 − x2 − 4x + 4 to describe the key features of g(x), including the end behavior. We can see that there are 3 x-intercepts at (2,0), (1,0) and (-2,0) which validates the point of Kelsey that the function can have as many as 3 zeros only because it is 3rd degree polynomial.
Part B)
As the second part of the new coaster is a parabola. To create a unique parabola in the pattern f(x) = ax2 + bx + c
finding derivative of g(x) picked in Part A) i.e.
g(x) = x3 − x2 − 4x + 4
g'(x)=3x2-2x-4
Graph of above is also attache.
From the graph we can see that its downwards directed parabola having vertex at (0.33, -4.33)
x-intercept at -0.87 and 1.53
y-intercept at (0,-4)
The axis of symmetry equation is a vertical line around which the parabola is symmetric is given by equation of a vertical line that passes through the vertex i.e. x=0.33
Part C)
Graph 3 is also attached.
Part D)
For a 15 seconds ad campaign, following features can be included:
Roller coaster that have a three rise
two sharp dips
the 2nd dip goes more deeper than the first one!
