Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Describing Graphs of Polynomial Functions

Describing Graphs of Polynomial Functions 1.15 - Solution

arrow_back Return to Describing Graphs of Polynomial Functions

We want to estimate the coordinates of every turning point. A turning point is either a relative maximum or minimum of the function. Let's look at the given graph to see where the turning points are.

As we can see above, the graph has two turning points around (-3,-1.5)(\text{-} 3,\text{-}1.5) and (0.5,-6.5).(0.5,\text{-}6.5). The point (-3,-1.5)(\text{-} 3,\text{-}1.5) corresponds to relative maximum and the point (0.5,-6.5)(0.5,\text{-}6.5) corresponds to relative minimum.

Next, we will estimate the zeros of the function. A zero is the x-x\text{-}coordinate of the point at which the graph intercepts the x-x\text{-}axis. Let's consider the given graph.

The zero occurs at approximately x=2.5.x=2.5.

Turning Points (-3,-1.5)(\text{-} 3,\text{-} 1.5) and (0.5,-6.5)(0.5,\text{-} 6.5)
Relative Maximum (-3,-1.5)(\text{-} 3,\text{-} 1.5)
Relative Minimum (0.5,-6.5)(0.5,\text{-}6.5)
Zero x=2.5x=2.5