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

1. 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=(x−2)2+3y=(x-2)^2+3?

Please select an answer first.

Correct answer: A

The correct answer is (2,3)(2,3).

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

Vertex form y = a(x-h)^2+k has vertex (h,k), so h = 2 and k = 3.

2. QuestionMultiple choice

What is the axis of symmetry of y=x2−6x+5y=x^2-6x+5?

Please select an answer first.

Correct answer: B

The correct answer is x=3x=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: For ax^2+bx+c, the axis is x = -b/(2a) = 6/2 = 3.
  3. Check the result: The correct answer is x=3x=3.

For ax^2+bx+c, the axis is x = -b/(2a) = 6/2 = 3.

3. QuestionMultiple choice

How does the graph of y=−2x2+1y=-2x^2+1 open?

Please select an answer first.

Correct answer: C

The correct answer is Downward.

  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 leading coefficient is negative, so the parabola opens downward.
  3. Check the result: The correct answer is Downward.

The leading coefficient is negative, so the parabola opens downward.

4. QuestionMultiple choice

What is the axis of symmetry of y=x2+4x+1y=x^2+4x+1?

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: Use x = -b/(2a): x = -4/2 = -2.
  3. Check the result: The correct answer is x=−2x=-2.

Use x = -b/(2a): x = -4/2 = -2.

5. QuestionMultiple choice

What is the vertex of y=3(x+1)2−4y=3(x+1)^2-4?

Please select an answer first.

Correct answer: A

The correct answer is (−1,−4)(-1,-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: Since x+1 = x-(-1), the vertex is (-1,-4).
  3. Check the result: The correct answer is (−1,−4)(-1,-4).

Since x+1 = x-(-1), the vertex is (-1,-4).

6. QuestionMultiple choice

What type of extremum does a quadratic with a>0a>0 have?

Please select an answer first.

Correct answer: B

The correct answer is A minimum.

  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 positive leading coefficient makes the parabola open upward, so its vertex is a minimum.
  3. Check the result: The correct answer is A minimum.

A positive leading coefficient makes the parabola open upward, so its vertex is a minimum.

7. QuestionMultiple choice

What is the x-coordinate of the vertex of y=(x−5)2−2y=(x-5)^2-2?

Please select an answer first.

Correct answer: C

The correct answer is 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: Vertex form shows h = 5 because x-5 = x-h.
  3. Check the result: The correct answer is 5.

Vertex form shows h = 5 because x-5 = x-h.

8. QuestionMultiple choice

How is y=(x+2)2−1y=(x+2)^2-1 transformed from y=x2y=x^2?

Please select an answer first.

Correct answer: D

The correct answer is Shift left 2 units and down 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: Replacing x with x+2 shifts left 2, and subtracting 1 shifts down 1.
  3. Check the result: The correct answer is Shift left 2 units and down 1 unit..

Replacing x with x+2 shifts left 2, and subtracting 1 shifts down 1.

9. QuestionMultiple choice

Compared with y=x2y=x^2, how does y=2x2y=2x^2 appear?

Please select an answer first.

Correct answer: A

The correct answer is Narrower.

  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 leading coefficient with absolute value greater than 1 vertically stretches the parabola, making it narrower.
  3. Check the result: The correct answer is Narrower.

A leading coefficient with absolute value greater than 1 vertically stretches the parabola, making it narrower.

10. QuestionMultiple choice

What is the expanded form of y=(x−3)2y=(x-3)^2?

Please select an answer first.

Correct answer: B

The correct answer is y=x2−6x+9y=x^2-6x+9.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Expand the square: (x-3)^2 = x^2 - 6x + 9.
  3. Check the result: The correct answer is y=x2−6x+9y=x^2-6x+9.

Expand the square: (x-3)^2 = x^2 - 6x + 9.

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