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Quadratic Functions Practice Tests

These Grade 11 Math practice tests develop quadratic-function skills across standard, factored, and vertex forms, including roots, discriminants, transformations, extrema, graph features, and real-world models.

Skills covered

  • Finding vertices, axes of symmetry, opening direction, maxima, and minima
  • Factoring quadratics and identifying x-intercepts, y-intercepts, and repeated roots
  • Using the discriminant and quadratic formula to classify and solve roots
  • Analyzing quadratic graphs, ranges, transformations, and completed-square form
  • Applying quadratic models to projectile motion, revenue, area, population, depreciation, and break-even contexts

How to use these practice tests

Choose the form that exposes the requested feature. Use vertex form for transformations and extrema, factored form for roots, and the quadratic formula or discriminant when factoring is not convenient.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Quadratic Functions Practice Tests

Practice Grade 11 Math questions about quadratic forms, vertices, axes of symmetry, roots, factoring, discriminants, graphs, and quadratic models.

Choose the best answer. Identify the quadratic form, use the appropriate formula or factorization, and interpret the vertex, roots, and graph in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the discriminant of ax2+bx+c=0ax^2+bx+c=0?

Please select an answer first.

Correct answer: A

The correct answer is b2−4acb^2-4ac.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: The discriminant is the expression b^2 - 4ac under the square root in the quadratic formula.
  3. Check the result: The correct answer is b2−4acb^2-4ac.

The discriminant is the expression b^2 - 4ac under the square root in the quadratic formula.

2. QuestionMultiple choice

What is the discriminant of x2+2x+5=0x^2+2x+5=0?

Please select an answer first.

Correct answer: B

The correct answer is -16.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Compute b^2-4ac = 2^2 - 4(1)(5) = 4 - 20 = -16.
  3. Check the result: The correct answer is -16.

Compute b^2-4ac = 2^2 - 4(1)(5) = 4 - 20 = -16.

3. QuestionMultiple choice

What does a negative discriminant indicate?

Please select an answer first.

Correct answer: C

The correct answer is Two nonreal complex roots.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: A negative discriminant gives a negative square root, producing two nonreal complex conjugate roots.
  3. Check the result: The correct answer is Two nonreal complex roots.

A negative discriminant gives a negative square root, producing two nonreal complex conjugate roots.

4. QuestionMultiple choice

What is the discriminant of x2−6x+9=0x^2-6x+9=0?

Please select an answer first.

Correct answer: D

The correct answer is 0.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Compute (-6)^2 - 4(1)(9) = 36 - 36 = 0.
  3. Check the result: The correct answer is 0.

Compute (-6)^2 - 4(1)(9) = 36 - 36 = 0.

5. QuestionMultiple choice

Solve x2−4x−5=0x^2-4x-5=0.

Please select an answer first.

Correct answer: A

The correct answer is x=5x=5 and x=−1x=-1.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Factor as (x-5)(x+1)=0, giving x=5 and x=-1.
  3. Check the result: The correct answer is x=5x=5 and x=−1x=-1.

Factor as (x-5)(x+1)=0, giving x=5 and x=-1.

6. QuestionMultiple choice

Solve 2x2+3x−2=02x^2+3x-2=0.

Please select an answer first.

Correct answer: B

The correct answer is x=12x=\frac{1}{2} and x=−2x=-2.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Factor as (2x-1)(x+2)=0, so x=1/2 or x=-2.
  3. Check the result: The correct answer is x=12x=\frac{1}{2} and x=−2x=-2.

Factor as (2x-1)(x+2)=0, so x=1/2 or x=-2.

7. QuestionMultiple choice

Solve 3x2−12x+12=03x^2-12x+12=0.

Please select an answer first.

Correct answer: C

The correct answer is x=2x=2 with multiplicity 2.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Divide by 3: x^2-4x+4=(x-2)^2, so x=2 is a repeated root.
  3. Check the result: The correct answer is x=2x=2 with multiplicity 2.

Divide by 3: x^2-4x+4=(x-2)^2, so x=2 is a repeated root.

8. QuestionMultiple choice

Solve x2+2x−8=0x^2+2x-8=0.

Please select an answer first.

Correct answer: D

The correct answer is x=2x=2 and x=−4x=-4.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Factor as (x+4)(x-2)=0, giving x=-4 and x=2.
  3. Check the result: The correct answer is x=2x=2 and x=−4x=-4.

Factor as (x+4)(x-2)=0, giving x=-4 and x=2.

9. QuestionMultiple choice

What is the discriminant of 4x2+4x+1=04x^2+4x+1=0?

Please select an answer first.

Correct answer: A

The correct answer is 0.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Compute b^2-4ac = 4^2 - 4(4)(1) = 16 - 16 = 0.
  3. Check the result: The correct answer is 0.

Compute b^2-4ac = 4^2 - 4(4)(1) = 16 - 16 = 0.

10. QuestionMultiple choice

Solve x2−2x−3=0x^2-2x-3=0.

Please select an answer first.

Correct answer: B

The correct answer is x=3x=3 and x=−1x=-1.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Factor as (x-3)(x+1)=0, so the roots are 3 and -1.
  3. Check the result: The correct answer is x=3x=3 and x=−1x=-1.

Factor as (x-3)(x+1)=0, so the roots are 3 and -1.

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