Systems with a quadratic: a line and a parabola, a line and a circle, two parabolas

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Jun slides the line y = 2x + c until it touches y = x² − 6x + 10 at exactly one point. What is c?

   -6
2. 2.

   Luz slides the line y = -2x + c until it touches y = x² + 4x + 1 at exactly one point. What is c?

   -8
3. 3.

   Milo slides the line y = 4x + c until it touches y = x² − 2x + 7 at exactly one point. What is c?

   -2
4. 4.

   Noah slides the line y = 4x + c until it touches y = x² + 8x + 20 at exactly one point. What is c?

   16
5. 5.

   On a grid, Ren draws a tossed ball's path, y = -x² + 9x, and a ramp, y = 2x + 10. How high is the higher of the two crossing points?

   20
6. 6.

   On a grid, Esme draws a rainbow arch, y = -x² + 5x, and a slide, y = -x + 5. How high is the higher of the two crossing points?

   4
7. 7.

   Jun solves x² + y² = 13 and y = x² − 1 by putting x² = y + 1 into the circle. How many points do they share?

   • Two points
   • No points
   • Four points
   • One point
8. 8.

   Luz solves x² + y² = 29 and y = x² + 1 by putting x² = y − 1 into the circle. How many points do they share?

   • One point
   • Two points
   • No points
   • Four points
9. 9.

   Milo solves x² + y² = 25 and y = x² − 5 by putting x² = y + 5 into the circle. How many points do they share?

   • No points
   • Two points
   • Three points
   • Four points, with a touch counted twice
10. 10.

    Noah solves x² + y² = 16 and y = x² − 4 by putting x² = y + 4 into the circle. How many points do they share?

    • Three points
    • No points
    • Four points
    • Two points