Grade 11 · Math · Algebra 2

11th grade Graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs worksheet

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Graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

1.
Bo's robot draws p(x) = (x − 1)³(x + 4). What does the graph do at x = 1?
- It crosses the x-axis at x = -1.
- It touches the x-axis at x = 1 and turns back.
- It touches the x-axis at x = -1 and turns back.
- It crosses the x-axis at x = 1.
2.
Esme sketches p(x) = x(x − 5)⁴ on a grid map. What does the graph do at x = 5?
- It crosses the x-axis at x = -5.
- It crosses the x-axis at x = 5.
- It touches the x-axis at x = 5 and turns back.
- It touches the x-axis at x = -5 and turns back.
3.
Jun sketches p(x) = (x + 6)³(x − 1)² in pencil. What does the graph do at x = -6?
- It touches the x-axis at x = -6 and turns back.
- It crosses the x-axis at x = -6.
- It crosses the x-axis at x = 6.
- It touches the x-axis at x = 6 and turns back.
4.
Kira graphs p(x) = 5x² − 2x³ + 1 on graph paper. What does the graph do far to the left and far to the right?
- Rises on the left and falls on the right.
- Falls on the left and rises on the right.
- Falls on both sides.
- Rises on both sides.
5.
Luz's robot graphs p(x) = 3x − x⁴ + 2x³. What does the graph do far to the left and far to the right?
- Rises on the left and falls on the right.
- Rises on both sides.
- Falls on the left and rises on the right.
- Falls on both sides.
6.
Milo sketches p(x) = -3x² + x⁵ − 4. What does the graph do far to the left and far to the right?
- Rises on the left and falls on the right.
- Rises on both sides.
- Falls on both sides.
- Falls on the left and rises on the right.
7.
Noah copies p(x) = 2x³ + 1 − x⁶ into a notebook. What does the graph do far to the left and far to the right?
- Rises on the left and falls on the right.
- Falls on the left and rises on the right.
- Rises on both sides.
- Falls on both sides.
Ren sketches p(x) = (x + 2)²(x − 3) on graph paper. What is the y-intercept of the graph?
Tala's robot plots p(x) = -(x − 3)²(x + 5). What is the y-intercept of the graph?
Bo sketches p(x) = 3(x − 2)²(x + 5) in pencil. What is the y-intercept of the graph?

11th grade Graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Graph polynomial functions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell where a graph crosses or touches the x-axis from its factors.
I can say what the ends of the graph do from the leading term.
I can match an equation to its graph and write one from a graph.

Standard: F-IF.C.7c, F-IF.B.4, A-APR.B.3

Words to know

end behavior: What the graph does far to the left and far to the right.

leading term: The term with the highest power of x.

touch: Meet the x-axis and turn back without crossing.

turning point: A point where the graph changes from rising to falling, or back.

range: Every output the graph reaches.

Common mistakes

Placed a zero on the wrong side of 0, reading x + 2 as the zero 2.

Treated a repeated factor as a single one, so a touching point became a crossing or the degree came out wrong.

Thought every repeated zero touches. Only an even power touches; an odd power like (x − 1)³ crosses.

What to say

Ask: what number makes x + 2 equal 0?

Ask: what does the little 2 in (x − 1)² tell you?

Ask: is (-1)³ negative?

Questions parents ask

What is the most common mistake with graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs?

Placed a zero on the wrong side of 0, reading x + 2 as the zero 2.

How can I help my child with graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs?

Ask: what number makes x + 2 equal 0?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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