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

Grade 11 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Jun tests the point (-2, 5) in the system y = x² + 1 and y = -x + 1. Which is true?

   • On neither
   • On the line only
   • On both, so it is a solution
   • On the parabola only
2. 2.

   Luz tests the point (3, 7) in the system y = x² − 2 and y = 2x + 1. Which is true?

   • On the line only
   • On both, so it is a solution
   • On the parabola only
   • On neither
3. 3.

   Milo tests the point (-3, 4) in the system y = x² − 5 and y = 2x + 10. Which is true?

   • On both, so it is a solution
   • On the line only
   • On the parabola only
   • On neither
4. 4.

   Pia sets y = x² + 2x − 3 equal to y = 4x + 5 and moves everything to one side. Which equation is that?

   • x² − 2x − 8 = 0
   • x² − 2x + 8 = 0
   • x² − 2x + 2 = 0
   • x² + 6x − 8 = 0
5. 5.

   Ren sets y = x² − x + 4 equal to y = 3x − 1 and moves everything to one side. Which equation is that?

   • x² − 4x + 3 = 0
   • x² − 4x − 5 = 0
   • x² + 2x + 5 = 0
   • x² − 4x + 5 = 0
6. 6.

   Esme sets y = x² − 4x − 2 equal to y = -x − 6 and moves everything to one side. Which equation is that?

   • x² − 3x − 4 = 0
   • x² − 3x − 8 = 0
   • x² − 5x + 4 = 0
   • x² − 3x + 4 = 0
7. 7.

   Jun puts a line into a parabola and gets x² − 4x + 5 = 0. How many points do the line and the parabola share?

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

   Luz puts a line into a parabola and gets x² + 6x + 9 = 0. How many points do the line and the parabola share?

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

   Milo puts a line into a parabola and gets x² − 2x − 8 = 0. How many points do the line and the parabola share?

   • Two points
   • One point
   • No points
10. 10.

    Noah puts a line into a parabola and gets x² − 10x + 25 = 0. How many points do the line and the parabola share?

    • No points
    • One point
    • Two points