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

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 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. 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. 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. 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. 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. 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. 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.
8. 8.

   Ren sketches p(x) = (x + 2)²(x − 3) on graph paper. What is the y-intercept of the graph?

   -12
9. 9.

   Tala's robot plots p(x) = -(x − 3)²(x + 5). What is the y-intercept of the graph?

   -45
10. 10.

    Bo sketches p(x) = 3(x − 2)²(x + 5) in pencil. What is the y-intercept of the graph?

    60