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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. 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

At what time does h(t)=−16t2+80t+6h(t)=-16t^2+80t+6 reach its maximum?

Please select an answer first.

Correct answer: A

The correct answer is t=2.5t=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 vertex time is -b/(2a) = -80/(2·-16) = 2.5.
  3. Check the result: The correct answer is t=2.5t=2.5.

The vertex time is -b/(2a) = -80/(2·-16) = 2.5.

2. QuestionMultiple choice

What is the maximum height of h(t)=−16t2+80t+6h(t)=-16t^2+80t+6?

Please select an answer first.

Correct answer: B

The correct answer is 106.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Substitute t=2.5: -16(2.5)^2 + 80(2.5) + 6 = -100 + 200 + 6 = 106.
  3. Check the result: The correct answer is 106.

Substitute t=2.5: -16(2.5)^2 + 80(2.5) + 6 = -100 + 200 + 6 = 106.

3. QuestionMultiple choice

At what production level is R(x)=−x2+24xR(x)=-x^2+24x maximized?

Please select an answer first.

Correct answer: C

The correct answer is x=12x=12.

  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 revenue vertex occurs at x=-b/(2a) = -24/(2·-1) = 12.
  3. Check the result: The correct answer is x=12x=12.

The revenue vertex occurs at x=-b/(2a) = -24/(2·-1) = 12.

4. QuestionMultiple choice

What are the break-even values for R(x)=−x2+10x−16R(x)=-x^2+10x-16?

Please select an answer first.

Correct answer: D

The correct answer is 2 and 8.

  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 R=0 and multiply by -1: x^2-10x+16=(x-2)(x-8), so x=2 and x=8.
  3. Check the result: The correct answer is 2 and 8.

Set R=0 and multiply by -1: x^2-10x+16=(x-2)(x-8), so x=2 and x=8.

5. QuestionMultiple choice

A rectangle has perimeter 30 and width x. Which width maximizes its area?

Please select an answer first.

Correct answer: A

The correct answer is 7.5.

  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 length is 15-x, so area x(15-x) has vertex at x=15/2=7.5.
  3. Check the result: The correct answer is 7.5.

The length is 15-x, so area x(15-x) has vertex at x=15/2=7.5.

6. QuestionMultiple choice

What is P(1)P(1) for P(t)=800(1.04)tP(t)=800(1.04)^t?

Please select an answer first.

Correct answer: B

The correct answer is 832.

  1. Identify the quadratic structure: Determine the coefficients, vertex, axis of symmetry, roots, discriminant, transformation, or model feature involved.
  2. Apply the quadratic relationship: Substitute t=1: P(1)=800(1.04)=832.
  3. Check the result: The correct answer is 832.

Substitute t=1: P(1)=800(1.04)=832.

7. QuestionMultiple choice

What is V(2)V(2) for V(t)=20000(0.85)tV(t)=20000(0.85)^t?

Please select an answer first.

Correct answer: C

The correct answer is 14450.

  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 20000(0.85)^2 = 20000(0.7225) = 14450.
  3. Check the result: The correct answer is 14450.

Compute 20000(0.85)^2 = 20000(0.7225) = 14450.

8. QuestionMultiple choice

What is the maximum value of h(t)=−4(t−3)2+40h(t)=-4(t-3)^2+40?

Please select an answer first.

Correct answer: D

The correct answer is 40.

  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 (3,40), and the negative coefficient means 40 is the maximum.
  3. Check the result: The correct answer is 40.

The vertex is (3,40), and the negative coefficient means 40 is the maximum.

9. QuestionMultiple choice

When does h(t)=−16t2+48th(t)=-16t^2+48t equal zero?

Please select an answer first.

Correct answer: A

The correct answer is t=0t=0 or t=3t=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 h(t)=-16t(t-3), so the zeros are t=0 and t=3.
  3. Check the result: The correct answer is t=0t=0 or t=3t=3.

Factor h(t)=-16t(t-3), so the zeros are t=0 and t=3.

10. QuestionMultiple choice

What is the maximum value of f(x)=−x2+6x+1f(x)=-x^2+6x+1?

Please select an answer first.

Correct answer: B

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: The vertex occurs at x=3, and f(3)=-9+18+1=10.
  3. Check the result: The correct answer is 10.

The vertex occurs at x=3, and f(3)=-9+18+1=10.

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