Grade 11 · Math · Algebra 2

11th grade Systems with a quadratic: a line and a parabola, a line and a circle, two parabolas worksheet

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Level: Building Confidence · On Level · Challenge Me

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

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

1.
Luz tests the point (3, 7) in the system y = x² − 2 and y = 2x + 1. Which is true?
- On the line only
- On neither
- On both, so it is a solution
- On the parabola only
2.
Milo tests the point (-3, 4) in the system y = x² − 5 and y = 2x + 10. Which is true?
- On neither
- On the parabola only
- On both, so it is a solution
- On the line only
3.
Noah tests the point (1, 4) in the system y = x² + 3 and y = 3x. Which is true?
- On both, so it is a solution
- On the parabola only
- On neither
- On the line only
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 + 2 = 0
- x² + 6x − 8 = 0
- x² − 2x − 8 = 0
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 − 4x − 5 = 0
- x² + 2x + 5 = 0
6.
Zee sets y = x² + 3x + 1 equal to y = -2x + 7 and moves everything to one side. Which equation is that?
- x² + 5x + 8 = 0
- x² + 5x + 6 = 0
- x² + x − 6 = 0
- x² + 5x − 6 = 0
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.
Luz puts a line into a parabola and gets x² + 6x + 9 = 0. How many points do the line and the parabola share?
- No points
- Two points
- One point
9.
Milo puts a line into a parabola and gets x² − 2x − 8 = 0. How many points do the line and the parabola share?
- No points
- Two points
- One point
10.
Noah puts a line into a parabola and gets x² − 10x + 25 = 0. How many points do the line and the parabola share?
- One point
- No points
- Two points

11th grade Systems with a quadratic: a line and a parabola, a line and a circle, two parabolas worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Systems with a quadratic: a line and a parabola, a line and a circle, two parabolas. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can check whether a point solves a system.
I can find every point where a line meets a parabola or a circle.
I can tell from the discriminant whether they meet twice, once or not at all.

Standard: A-REI.C.7

Words to know

system: Two equations that must both be true at once.

substitute: Put one rule in place of y in the other.

meeting point: A point on both graphs: a row where the outputs match.

touch: Meet at exactly one point, with discriminant 0.

Common mistakes

Your child checked the point in one equation only.

Your child made the square of a negative number negative.

Your child doubled x instead of squaring it.

What to say

Ask: does the point fit the other equation too?

Ask: what is (-3) × (-3)?

Ask: is 3² the same as 2 × 3?

Questions parents ask

What is the most common mistake with systems with a quadratic: a line and a parabola, a line and a circle, two parabolas?

Your child checked the point in one equation only.

How can I help my child with systems with a quadratic: a line and a parabola, a line and a circle, two parabolas?

Ask: does the point fit the other equation too?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

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