Features of a parabola from its graph or its equation

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Kira graphs a fountain's arc, y = -2x² + 20x - 7. What is the axis of symmetry? Write the number after x =.

   5
2. 2.

   Luz graphs a salad bowl, y = 4x² + 24x + 5 (no croutons on the graph). What is the axis of symmetry? Write the number after x =.

   -3
3. 3.

   Noah graphs a toy rocket path, y = -x² + 6x + 1. Does the graph have a maximum or a minimum, and what is it?

   • A minimum of 10
   • A maximum of 1
   • A maximum of 10
   • A maximum of 3
4. 4.

   Pia graphs a dip in a trail map, y = x² + 10x + 19. Does the graph have a maximum or a minimum, and what is it?

   • A maximum of -6
   • A minimum of -5
   • A minimum of -6
   • A minimum of 19
5. 5.

   Zee graphs a fruit bowl, y = x² - 4x + 7. What are the domain and range of the graph?

   • Domain: all real numbers; range: y ≥ 7
   • Domain: all real numbers; range: y ≤ 3
   • Domain: all real numbers; range: y ≥ 3
   • Domain: x ≥ 2; range: y ≥ 3
6. 6.

   Ari graphs a rainbow, y = -x² - 2x + 5. What are the domain and range of the graph?

   • Domain: all real numbers; range: y ≤ 5
   • Domain: x ≥ -1; range: y ≤ 6
   • Domain: all real numbers; range: y ≤ 6
   • Domain: all real numbers; range: y ≥ 6
7. 7.

   Bo graphs a skate ramp, y = 3x² + 12x + 2. What are the domain and range of the graph?

   • Domain: x ≥ -2; range: y ≥ -10
   • Domain: all real numbers; range: y ≤ -10
   • Domain: all real numbers; range: y ≥ 2
   • Domain: all real numbers; range: y ≥ -10
8. 8.

   Esme graphs a ball toss, y = -2x² + 8x - 1 (the ball came back down, eventually). What are the domain and range of the graph?

   • Domain: all real numbers; range: y ≤ -1
   • Domain: all real numbers; range: y ≤ 7
   • Domain: all real numbers; range: y ≥ 7
   • Domain: x ≥ 2; range: y ≤ 7
9. 9.

   Kira graphs a whale's jump, y = -x² - 4x + 1 (splash!). For which inputs is the graph increasing?

   • x < 5
   • x > -2
   • x < -2
10. 10.

    Luz graphs a sled run into a dip, y = 2x² + 4x - 1. For which inputs is the graph decreasing?

    • x > -1
    • x < -1
    • x < -3