Graphing Polynomial Functions - State the maximum number of turns, real zeros, and extrema to the nearest tenth

Oct 8, 2026

Uploaded by Mia

Worksheet for graphing polynomial functions in Infinite Algebra 2. Students analyze each given function by determining the maximum number of turns the graph could make, identifying the number of real zeros, and approximating each zero to the nearest tenth. The task also requires sketching the graph and estimating the relative minima and relative maxima values to the nearest tenth, with results recorded for multiple numbered problems.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Graphing Polynomial Functions

Maximum number of turns

Real zeros and approximations

Relative minima and relative maxima

Kuta Software-Infinite Algebra 2 Name Graphing Polynomial Functions Date Period State the maximum number of turns the graph of each function could make. Then sketch the graph. State the number of real zeros. Approximate each zero to the nearest tenth. Approximate the relative minima and relative maxima to the nearest tenth. 1) f (x) = x 􀀕 􀀎 􀀕x 􀀐 􀀘 3) f (x) = x 􀀗 􀀐 􀀗x 􀀖 􀀎 􀀕x 􀀕 􀀎 x 􀀎 􀀗 2) f (x) = 􀀐x􀀗 􀀎 x 􀀖 􀀎 􀀕x 􀀕 4) f (x) = x 􀀖 􀀎 x 􀀕 􀀐 x 􀀐 􀀕 5) f (x) = x 􀀘 􀀐 􀀗x 􀀖 􀀎 􀀗x 􀀐 􀀔 7) f (x) = 􀀐x􀀘 􀀎 􀀗x 􀀖 􀀐 􀀘x 􀀐 􀀕 6) f (x) = x 􀀖 􀀎 􀀔􀀔 x 􀀕 􀀎 􀀖􀀘 x 􀀎 􀀖􀀕 8) f (x) = x 􀀗 􀀐 x 􀀕 􀀎 x Kuta Software-Infinite Algebra 2 Name Graphing Polynomial Functions Date Period State the maximum number of turns the graph of each function could make. Then sketch the graph. State the number of real zeros. Approximate each zero to the nearest tenth. Approximate the relative minima and relative maxima to the nearest tenth. 1) f (x) = x 􀀕 􀀎 􀀕x 􀀐 􀀘 Max \# Turns: 1 \# Real Zeros: 2 Real Zeros: 􀀐􀀖􀀑􀀗 , 􀀔􀀑􀀗 Minima: (􀀐􀀔 , 􀀐􀀙) Maxima: None 2) f (x) = 􀀐x􀀗 􀀎 x 􀀖 􀀎 􀀕x 􀀕 Max \# Turns: 3 \# Real Zeros: 3 Real Zeros: 􀀐􀀔 , 􀀓 , 􀀕 Minima: (􀀓 , 􀀓) Maxima: (􀀐􀀓􀀑􀀚 , 􀀓􀀑􀀗) (􀀔􀀑􀀗 , 􀀕􀀑􀀛) 5) f (x) = x 􀀘 􀀐 􀀗x 􀀖 􀀎 􀀗x 􀀐 􀀔 Max \# Turns: 4 \# Real Zeros: 3 Real Zeros: 􀀓􀀑􀀖 , 􀀔􀀑􀀚 , 􀀔 Minima: (􀀐􀀓􀀑􀀙 , 􀀐􀀕􀀑􀀙) (􀀔􀀑􀀗 , 􀀐􀀔) Maxima: (􀀐􀀔􀀑􀀗 , 􀀐􀀔) (􀀓􀀑􀀙 , 􀀓􀀑􀀙) 6) f (x) = x 􀀖 􀀎 􀀔􀀔 x 􀀕 􀀎 􀀖􀀘 x 􀀎 􀀖􀀕 Max \# Turns: 2 \# Real Zeros: 3 Real Zeros: 􀀐􀀙􀀑􀀕 , 􀀐􀀖􀀑􀀕 , 􀀐􀀔􀀑􀀙 Minima: (􀀐􀀕􀀑􀀖 , 􀀐􀀕􀀑􀀘) Maxima: (􀀐􀀘 , 􀀚) 7) f (x) = 􀀐x􀀘 􀀎 􀀗x 􀀖 􀀐 􀀘x 􀀐 􀀕 Max \# Turns: 4 \# Real Zeros: 3 Real Zeros: 􀀐􀀔􀀑􀀙 , 􀀐􀀔 , 􀀐􀀓􀀑􀀘 Minima: (􀀐􀀔􀀑􀀗 , 􀀐􀀓􀀑􀀙) (􀀓􀀑􀀚 , 􀀐􀀗􀀑􀀖) Maxima: (􀀐􀀓􀀑􀀚 , 􀀓􀀑􀀖) (􀀔􀀑􀀗 , 􀀐􀀖􀀑􀀗) 8) f (x) = x 􀀗 􀀐 x 􀀕 􀀎 x Max \# Turns: 3 \# Real Zeros: 2 Real Zeros: 􀀐􀀔􀀑􀀖 , 􀀓 Minima: (􀀐􀀓􀀑􀀜 , 􀀐􀀔􀀑􀀔) Maxima: None Create your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

What is the first step for each polynomial function on the worksheet?

Determine the maximum number of turns the graph could make, based on the function’s degree and end behavior rules used in algebra 2 graphing.

How are the zeros required to be reported?

State the number of real zeros, then approximate each real zero to the nearest tenth.

What should students do with relative minima and maxima?

Approximate the relative minima and relative maxima to the nearest tenth and include them in the graph sketch results.

Oct 8, 2026

Uploaded by Mia