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.

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

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

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

Predicting Equations

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?

Predicting Equations

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 1+3 1+1 1−2 2 16=𝑎 4 2 −1 2 16=8𝑎 𝑎=2 𝑝 𝑥 =2 𝑥+3 𝑥+1 𝑥−2 2 (𝟏,𝟏𝟔)

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.