NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

4. Test

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 vertex of y=−x2+4x+1y=-x^2+4x+1?

Please select an answer first.

Correct answer: A

The correct answer is (2,5)(2,5).

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: The axis is x=2, and y=-2^2+4(2)+1=5, so the vertex is (2,5).
  3. Check the result: The correct answer is (2,5)(2,5).

The axis is x=2, and y=-2^2+4(2)+1=5, so the vertex is (2,5).

2. QuestionMultiple choice

What is the maximum value of y=−2(x−3)2+7y=-2(x-3)^2+7?

Please select an answer first.

Correct answer: B

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 parabola opens downward and its vertex is (3,7), so the maximum value is 7.
  3. Check the result: The correct answer is 7.

The parabola opens downward and its vertex is (3,7), so the maximum value is 7.

3. QuestionMultiple choice

What is the minimum value of y=12(x+4)2−2y=\frac{1}{2}(x+4)^2-2?

Please select an answer first.

Correct answer: C

The correct answer is -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 parabola opens upward and has vertex (-4,-2), so the minimum value is -2.
  3. Check the result: The correct answer is -2.

The parabola opens upward and has vertex (-4,-2), so the minimum value is -2.

4. QuestionMultiple choice

What is the range of y=(x−1)2+2y=(x-1)^2+2?

Please select an answer first.

Correct answer: D

The correct answer is y≥2y\ge2.

  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 vertex is (1,2) and the parabola opens upward, so y cannot be less than 2.
  3. Check the result: The correct answer is y≥2y\ge2.

The vertex is (1,2) and the parabola opens upward, so y cannot be less than 2.

5. QuestionMultiple choice

What is the range of y=−3(x+2)2+4y=-3(x+2)^2+4?

Please select an answer first.

Correct answer: A

The correct answer is y≤4y\le4.

  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 vertex is (-2,4) and the parabola opens downward, so 4 is the maximum.
  3. Check the result: The correct answer is y≤4y\le4.

The vertex is (-2,4) and the parabola opens downward, so 4 is the maximum.

6. QuestionMultiple choice

What is the vertex of y=x2+8x+10y=x^2+8x+10?

Please select an answer first.

Correct answer: B

The correct answer is (−4,−6)(-4,-6).

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Complete the square: x^2+8x+10=(x+4)^2-6, so the vertex is (-4,-6).
  3. Check the result: The correct answer is (−4,−6)(-4,-6).

Complete the square: x^2+8x+10=(x+4)^2-6, so the vertex is (-4,-6).

7. QuestionMultiple choice

What is the solution to x2−4x+4=0x^2-4x+4=0?

Please select an answer first.

Correct answer: C

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: Factor as (x-2)^2=0, giving the repeated solution x=2.
  3. Check the result: The correct answer is x=2x=2.

Factor as (x-2)^2=0, giving the repeated solution x=2.

8. QuestionMultiple choice

What are the x-intercepts of y=(x+1)2−9y=(x+1)^2-9?

Please select an answer first.

Correct answer: D

The correct answer is 2 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: Set y=0: (x+1)^2=9, so x+1=±3 and x=2 or -4.
  3. Check the result: The correct answer is 2 and -4.

Set y=0: (x+1)^2=9, so x+1=±3 and x=2 or -4.

9. QuestionMultiple choice

What transformation does y=(x−2)2+1y=(x-2)^2+1 apply to y=x2y=x^2?

Please select an answer first.

Correct answer: A

The correct answer is Shift right 2 units and up 1 unit..

  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 x-2 shifts right 2, and +1 shifts up 1.
  3. Check the result: The correct answer is Shift right 2 units and up 1 unit..

The x-2 shifts right 2, and +1 shifts up 1.

10. QuestionMultiple choice

At what time is the maximum reached for h(t)=−16t2+64t+2h(t)=-16t^2+64t+2?

Please select an answer first.

Correct answer: B

The correct answer is t=2t=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 vertex time is -b/(2a) = -64/(2·-16) = 2.
  3. Check the result: The correct answer is t=2t=2.

The vertex time is -b/(2a) = -64/(2·-16) = 2.

Previous testNext test