1. I can write the equation of a
polynomial from a graph
Warm Up
Write the equation of the parabola with a vertex of (−𝟑,𝟔) that goes through the point (𝟏,−𝟐).
2) Write a possible equation for a polynomial that “bounces” off the x-axis at −𝟏 and has an x-intercept of 𝟒.

2. Warm Up
Write the equation of the parabola with a vertex of (−𝟑,𝟔) that goes through the point (𝟏,−𝟐).

3. Warm Up
Write a possible equation for a polynomial that “bounces” off the x-axis at −𝟏 and has an x-intercept of 𝟒.

4. Predicting Equations
The number of “turns” in a graph helps determine the degree of the graph.
A 3rd degree polynomial has, at most, 2 turns
A 6th degree polynomial has, at most, 5 turns
Knowing the number of turns in a graph also tells you the minimum degree of the graph
A graph with 5 turns is at least a 6th degree polynomial

5. Predicting Equations Two turns Three turns Minimum 3rd Degree
Minimum 4th Degree

6. Predicting Equations

7. Does the equation work for our graph?
Predicting Equations
𝒚=𝒙(𝒙+𝟑)(𝒙−𝟐)
𝒚=− 𝒙 𝟑 (𝒙+𝟑)(𝒙−𝟐)
𝒚=− (𝐱+𝟐) 𝟐 (𝐱−𝟏)
How can we check?
Does the equation work for our graph?

8. Predicting Equations

9. Predicting Equations 𝑝 𝑥 =𝑎 𝑥+3 𝑥+1 𝑥−2 2 16= 𝑎 1+3 1+1 1−2 2
𝑝 𝑥 =𝑎 𝑥+3 𝑥+1 𝑥−2 2
16= 𝑎 −2 2
16=𝑎 −1 2
16=8𝑎
𝑎=2
𝑝 𝑥 =2 𝑥+3 𝑥+1 𝑥−2 2
(𝟏,𝟏𝟔)

10. Write the exact equation for the graph in problem 9-47 c.
Homework
Write the exact equation for the graph in problem 9-47 c.