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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 are the roots of x2−5x+6=0x^2-5x+6=0?

Please select an answer first.

Correct answer: A

The correct answer is 2 and 3.

  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 x^2-5x+6 as (x-2)(x-3), so the roots are 2 and 3.
  3. Check the result: The correct answer is 2 and 3.

Factor x^2-5x+6 as (x-2)(x-3), so the roots are 2 and 3.

2. QuestionMultiple choice

What are the roots of x2+7x+12=0x^2+7x+12=0?

Please select an answer first.

Correct answer: B

The correct answer is -3 and -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+3)(x+4), so the roots are -3 and -4.
  3. Check the result: The correct answer is -3 and -4.

Factor as (x+3)(x+4), so the roots are -3 and -4.

3. QuestionMultiple choice

Solve x2−9=0x^2-9=0.

Please select an answer first.

Correct answer: C

The correct answer is x=±3x=\pm3.

  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 difference of squares gives (x-3)(x+3)=0, so x=±3.
  3. Check the result: The correct answer is x=±3x=\pm3.

The difference of squares gives (x-3)(x+3)=0, so x=±3.

4. QuestionMultiple choice

What is the repeated root of x2+4x+4=0x^2+4x+4=0?

Please select an answer first.

Correct answer: D

The correct answer is 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: The expression is (x+2)^2, so the repeated root is -2.
  3. Check the result: The correct answer is x=−2x=-2.

The expression is (x+2)^2, so the repeated root is -2.

5. QuestionMultiple choice

What is the factored form of x2+x−12x^2+x-12?

Please select an answer first.

Correct answer: A

The correct answer is (x+4)(x−3)(x+4)(x-3).

  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 factors 4 and -3 multiply to -12 and add to 1.
  3. Check the result: The correct answer is (x+4)(x−3)(x+4)(x-3).

The factors 4 and -3 multiply to -12 and add to 1.

6. QuestionMultiple choice

What are the roots of 2x2−8x=02x^2-8x=0?

Please select an answer first.

Correct answer: B

The correct answer is 0 and 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 2x(x-4)=0, giving x=0 or x=4.
  3. Check the result: The correct answer is 0 and 4.

Factor 2x(x-4)=0, giving x=0 or x=4.

7. QuestionMultiple choice

What is the y-intercept of y=x2−4x+7y=x^2-4x+7?

Please select an answer first.

Correct answer: C

The correct answer is 7.

  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 y-intercept occurs at x=0, so y=7.
  3. Check the result: The correct answer is 7.

The y-intercept occurs at x=0, so y=7.

8. QuestionMultiple choice

What are the x-intercepts of y=(x−1)(x+5)y=(x-1)(x+5)?

Please select an answer first.

Correct answer: D

The correct answer is 1 and -5.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Set each factor equal to zero: x-1=0 or x+5=0.
  3. Check the result: The correct answer is 1 and -5.

Set each factor equal to zero: x-1=0 or x+5=0.

9. QuestionMultiple choice

What is the sum of the roots of x2−10x+21=0x^2-10x+21=0?

Please select an answer first.

Correct answer: A

The correct answer is 10.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: By Vieta's formula, the sum is -b/a = -(-10)/1 = 10.
  3. Check the result: The correct answer is 10.

By Vieta's formula, the sum is -b/a = -(-10)/1 = 10.

10. QuestionMultiple choice

What are the roots of x2−2x−8=0x^2-2x-8=0?

Please select an answer first.

Correct answer: B

The correct answer is 4 and -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 (x-4)(x+2), so the roots are 4 and -2.
  3. Check the result: The correct answer is 4 and -2.

Factor as (x-4)(x+2), so the roots are 4 and -2.

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