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Quadratic Equations Introduction Practice Tests

These Grade 9 Math practice tests cover quadratic standard form, coefficients, degree, factoring, the zero-product property, square roots, roots and zeros, parabolas, vertex form, axis of symmetry, intercepts, applications, and the discriminant.

Skills covered

  • Identifying a, b, c, degree, leading coefficient, and standard form
  • Expanding and factoring quadratic expressions
  • Solving quadratic equations by square roots and factoring
  • Reading vertex, intercept, opening, and symmetry information from parabolas
  • Using the discriminant and quadratic models to reason about real solutions

How to use these practice tests

Rewrite the equation in standard form, look for a common factor or recognizable pattern, apply the zero-product property when factoring, and verify each root in the original equation. For graphs, connect the coefficient and vertex form to opening, intercepts, and symmetry.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Quadratic Equations Introduction Practice Tests

Practice Grade 9 Math questions about quadratic standard form, coefficients, factoring, roots, zero-product reasoning, parabolas, vertices, intercepts, and the discriminant.

Choose the best answer. Identify the quadratic structure, select a suitable solving method, use exact forms when needed, and check roots in the original equation.

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

Solve x2=49x^2=49

Please select an answer first.

Correct answer: A

The correct answer is x = 7 or x = -7.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Both 7 and -7 have square 49.
  3. Check the result: The correct choice is x = 7 or x = -7.

Both 7 and -7 have square 49.

2. QuestionMultiple choice

Solve (x−2)2=16(x-2)^2=16

Please select an answer first.

Correct answer: B

The correct answer is x = 6 or x = -2.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Take both square roots: x - 2 = 4 or x - 2 = -4, giving x = 6 or -2.
  3. Check the result: The correct choice is x = 6 or x = -2.

Take both square roots: x - 2 = 4 or x - 2 = -4, giving x = 6 or -2.

3. QuestionMultiple choice

Solve x2+2x−8=0x^2+2x-8=0

Please select an answer first.

Correct answer: C

The correct answer is x = 2 or x = -4.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor as (x + 4)(x - 2) = 0, so the roots are -4 and 2.
  3. Check the result: The correct choice is x = 2 or x = -4.

Factor as (x + 4)(x - 2) = 0, so the roots are -4 and 2.

4. QuestionMultiple choice

Solve 2x2−8x=02x^2-8x=0

Please select an answer first.

Correct answer: D

The correct answer is x = 0 or x = 4.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor 2x(x - 4) = 0, giving x = 0 or x = 4.
  3. Check the result: The correct choice is x = 0 or x = 4.

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

5. QuestionMultiple choice

A height model is h=−16t2+64th=-16t^2+64t. At what time is the maximum height reached?

Please select an answer first.

Correct answer: A

The correct answer is 2 seconds.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The vertex time is -b/(2a) = -64/(2(-16)) = 2 seconds.
  3. Check the result: The correct choice is 2 seconds.

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

6. QuestionMultiple choice

In a height model, what do the x-intercepts usually represent?

Please select an answer first.

Correct answer: B

The correct answer is Times when the object is at ground level..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: A height of zero occurs when the object is on the ground, so the roots represent those times.
  3. Check the result: The correct choice is Times when the object is at ground level..

A height of zero occurs when the object is on the ground, so the roots represent those times.

7. QuestionMultiple choice

A revenue model is R=−x2+10xR=-x^2+10x. At which values is the revenue zero?

Please select an answer first.

Correct answer: C

The correct answer is x = 0 or x = 10.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor -x(x - 10) = 0, so x = 0 or x = 10.
  3. Check the result: The correct choice is x = 0 or x = 10.

Factor -x(x - 10) = 0, so x = 0 or x = 10.

8. QuestionMultiple choice

Solve x2−2x−15=0x^2-2x-15=0

Please select an answer first.

Correct answer: D

The correct answer is x = 5 or x = -3.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Factor as (x - 5)(x + 3) = 0, giving roots 5 and -3.
  3. Check the result: The correct choice is x = 5 or x = -3.

Factor as (x - 5)(x + 3) = 0, giving roots 5 and -3.

9. QuestionMultiple choice

How many real solutions does (x−4)2=0(x-4)^2=0 have?

Please select an answer first.

Correct answer: A

The correct answer is One real solution, x = 4..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The repeated factor x - 4 gives one distinct real root, x = 4.
  3. Check the result: The correct choice is One real solution, x = 4..

The repeated factor x - 4 gives one distinct real root, x = 4.

10. QuestionMultiple choice

Which value verifies that x = 3 is a root of x2−5x+6=0x^2-5x+6=0?

Please select an answer first.

Correct answer: B

The correct answer is The left side equals 0..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: Substitute 3: 3 squared - 5(3) + 6 = 9 - 15 + 6 = 0.
  3. Check the result: The correct choice is The left side equals 0..

Substitute 3: 3 squared - 5(3) + 6 = 9 - 15 + 6 = 0.

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