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

Grade 11 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Kira copies a graph from a math club poster. Which equation matches it?

   • (x + 2)(x − 3)²
   • -2(x − 2)(x + 3)²
   • 2(x + 2)(x − 3)²
   • -6(x + 2)(x − 3)
2. 2.

   Milo draws a graph from a table of values. Which equation matches it?

   • -3(x + 3)(x − 6)
   • (x + 3)²(x − 6)
   • (x − 3)²(x + 6)
   • -(x + 3)²(x − 6)
3. 3.

   Noah finds a graph on a grid map. Which equation matches it?

   • (x − 1)(x + 1)(x − 4)²
   • -8(x − 1)(x + 1)(x − 4)
   • 2(x − 1)(x + 1)(x − 4)²
   • 2(x + 1)(x − 1)(x + 4)²
4. 4.

   Ren sketches p(x) = -x(x − 5)²(x + 4) on graph paper. Which description fits the graph?

   • It crosses the x-axis at -4 and 0, touches it at 5, and rises on both sides.
   • It crosses the x-axis at -4 and 0, touches it at 5, and falls on both sides.
   • It crosses the x-axis at -4, 0 and 5, and falls on both sides.
   • It crosses the x-axis at 0 and 4, touches it at -5, and falls on both sides.
5. 5.

   Tala's robot graphs p(x) = 2(x − 3)(x + 1)². Which description fits the graph?

   • It crosses the x-axis at 3, touches it at -1, and falls on the left and rises on the right.
   • It crosses the x-axis at -1 and 3, and falls on the left and rises on the right.
   • It crosses the x-axis at 3, touches it at -1, and rises on the left and falls on the right.
   • It crosses the x-axis at -3, touches it at 1, and falls on the left and rises on the right.
6. 6.

   Zee sketches p(x) = -(x + 4)²(x − 1)(x − 5) in pencil. Which description fits the graph?

   • It crosses the x-axis at -5 and -1, touches it at 4, and falls on both sides.
   • It crosses the x-axis at 1 and 5, touches it at -4, and rises on both sides.
   • It crosses the x-axis at -4, 1 and 5, and falls on both sides.
   • It crosses the x-axis at 1 and 5, touches it at -4, and falls on both sides.
7. 7.

   Bo plans p(x) = 3(x + 2)(x − 6)² on a grid map. Which description fits the graph?

   • It crosses the x-axis at -2, touches it at 6, and falls on the left and rises on the right.
   • It crosses the x-axis at -2, touches it at 6, and rises on the left and falls on the right.
   • It crosses the x-axis at 2, touches it at -6, and falls on the left and rises on the right.
   • It crosses the x-axis at -2 and 6, and falls on the left and rises on the right.
8. 8.

   Esme graphs p(x) = (7 − x)(x + 2)². 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 both sides.
   • Rises on the left and falls on the right.
9. 9.

   Jun's robot graphs p(x) = (3 − x)²(x + 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 the left and rises on the right.
   • Falls on both sides.
10. 10.

    Kira sketches p(x) = (1 − x)³(x + 2)². What does the graph do far to the left and far to the right?

    • Falls on both sides.
    • Rises on both sides.
    • Rises on the left and falls on the right.
    • Falls on the left and rises on the right.