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

Grade 11 Math Worksheet

NameDate

Circle the best answer.

1.
Ren solves the system y = x² + 2x − 1 and y = x + 1. Which lists every solution?
- (-2, -1) and (1, 2)
- (1, 2)
- (-2, 0) and (1, 0)
- (2, -1) and (-1, 2)
2.
Zee solves the system y = -x² + 4 and y = x − 2. Which lists every solution?
- (-3, 0) and (2, 0)
- (-3, -5) and (2, 0)
- (2, 0)
- (3, -5) and (-2, 0)
3.
Esme solves the system y = x² − 4x + 1 and y = -2x + 4. Which lists every solution?
- (1, 6) and (-3, -2)
- (3, -2)
- (-1, 6) and (3, -2)
- (-1, 0) and (3, 0)
4.
Jun solves the system x² + y² = 25 and y = x + 1. Which lists every solution?
- (3, 4)
- (-4, 3) and (3, 4)
- (-4, -3) and (3, 4)
- (-3, -4) and (4, 3)
5.
Milo solves the system x² + y² = 10 and y = 2x − 5. Which lists every solution?
- (-3, 1) and (1, 3)
- (1, 3) and (3, 1)
- (3, 1)
- (1, -3) and (3, 1)
6.
Noah solves the system x² + y² = 13 and y = x + 1. Which lists every solution?
- (-2, -3) and (3, 2)
- (-3, 2) and (2, 3)
- (2, 3)
- (-3, -2) and (2, 3)
7.
Pia solves the system y = x² + 2x − 1 and y = -x² + 4x + 3 by subtracting. Which lists every solution?
- (2, 7)
- (-1, 2) and (2, -7)
- (-1, 0) and (2, 0)
- (-1, -2) and (2, 7)
8.
Ren solves the system y = x² − 3 and y = -x² + 2x + 1 by subtracting. Which lists every solution?
- (-1, 0) and (2, 0)
- (-1, -2) and (2, 1)
- (-1, 2) and (2, -1)
- (2, 1)
9.
Zee solves the system y = 2x² − 3x and y = x² + x − 3 by subtracting. Which lists every solution?
- (1, 1) and (3, -9)
- (1, -1) and (3, 9)
- (1, 0) and (3, 0)
- (3, 9)
10.
Esme solves the system y = x² + x and y = -x² − x + 4 by subtracting. Which lists every solution?
- (-2, 2) and (1, 2)
- (1, 2)
- (-2, -2) and (1, -2)
- (-2, 0) and (1, 0)

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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