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

NameDate

Circle the best answer.

1.
Esme finds a graph on a math club poster. Which equation matches it?
- (x + 3)(x − 1)(x − 4)
- (x + 3)(x − 1)²(x − 4)
- (x − 3)(x + 1)²(x + 4)
- -(x + 3)(x − 1)²(x − 4)
2.
Jun's robot prints a graph and its features. Which equation matches it?
- -(x − 4)²(x + 2)
- -(x + 4)(x − 2)
- -(x + 4)²(x − 2)
- (x + 4)²(x − 2)
3.
Kira sketches a graph from a table of values. Which equation matches it?
- x(x + 5)(x − 2)²
- -x(x + 5)(x − 2)
- -x(x + 5)(x − 2)²
- -x(x − 5)(x + 2)²
4.
Milo studies p(x) = -(x − 1)²(x + 3)³ on graph paper. What does the graph do far to the left and far to the right?
- Falls on both sides.
- Rises on both sides.
- Falls on the left and rises on the right.
- Rises on the left and falls on the right.
5.
Noah's robot graphs p(x) = 2x³(x + 6)⁴. What does the graph do far to the left and far to the right?
- Falls on both sides.
- Falls on the left and rises on the right.
- Rises on the left and falls on the right.
- Rises on both sides.
6.
Ren sketches p(x) = 4(x + 2)²(x − 5). 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.
7.
Tala plans p(x) = -x²(x − 7)³(x + 1) on a grid map. What does the graph do far to the left and far to the right?
- Rises on both sides.
- Falls on both sides.
- Rises on the left and falls on the right.
- Falls on the left and rises on the right.
8.
Zee graphs p(x) = x³ − 12x on graph paper. What is the range of p?
- All real numbers
- y ≥ -16
- -2 ≤ y ≤ 2
- -16 ≤ y ≤ 16
9.
Bo's robot graphs p(x) = -x³ + 27x. What is the range of p?
- -3 ≤ y ≤ 3
- y ≤ 54
- -54 ≤ y ≤ 54
- All real numbers
10.
Jun sketches p(x) = -x⁴ + 18x² − 5 on a grid map. What is the range of p?
- All real numbers
- y ≥ 76
- y ≤ 76
- y ≤ 3

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.

More algebra 2

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