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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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3. Test

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

Which way does the graph of y=x2y=x^2 open?

Please select an answer first.

Correct answer: A

The correct answer is Upward..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The leading coefficient is positive, so the parabola opens upward.
  3. Check the result: The correct choice is Upward..

The leading coefficient is positive, so the parabola opens upward.

2. QuestionMultiple choice

Which way does the graph of y=−x2y=-x^2 open?

Please select an answer first.

Correct answer: B

The correct answer is Downward..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The leading coefficient is negative, so the parabola opens downward.
  3. Check the result: The correct choice is Downward..

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

3. QuestionMultiple choice

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

Please select an answer first.

Correct answer: C

The correct answer is (2, 3).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: In vertex form y = (x - h) squared + k, the vertex is (h, k) = (2, 3).
  3. Check the result: The correct choice is (2, 3).

In vertex form y = (x - h) squared + k, the vertex is (h, k) = (2, 3).

4. QuestionMultiple choice

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

Please select an answer first.

Correct answer: D

The correct answer is (-1, -4).

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

Rewrite x + 1 as x - (-1), so h = -1 and k = -4.

5. QuestionMultiple choice

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

Please select an answer first.

Correct answer: A

The correct answer is x=3x=3.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The axis of symmetry of a vertex-form parabola is x = h, so x = 3.
  3. Check the result: The correct choice is x=3x=3.

The axis of symmetry of a vertex-form parabola is x = h, so x = 3.

6. QuestionMultiple choice

What are the x-intercepts of y=x2−4y=x^2-4?

Please select an answer first.

Correct answer: B

The correct answer is (-2, 0) and (2, 0).

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

Set y = 0: x squared - 4 = 0, so x = ±2.

7. QuestionMultiple choice

What is the y-intercept of y=x2+5y=x^2+5?

Please select an answer first.

Correct answer: C

The correct answer is (0, 5).

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

Set x = 0: y = 5, giving the point (0, 5).

8. QuestionMultiple choice

What is the vertex of y=x2y=x^2?

Please select an answer first.

Correct answer: D

The correct answer is (0, 0).

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: The basic parabola y = x squared has its minimum at the origin.
  3. Check the result: The correct choice is (0, 0).

The basic parabola y = x squared has its minimum at the origin.

9. QuestionMultiple choice

What happens when the absolute value of a in y=ax2y=ax^2 is greater than 1?

Please select an answer first.

Correct answer: A

The correct answer is The parabola is narrower than y = x squared..

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: A larger absolute leading coefficient makes the parabola steeper and narrower.
  3. Check the result: The correct choice is The parabola is narrower than y = x squared..

A larger absolute leading coefficient makes the parabola steeper and narrower.

10. QuestionMultiple choice

What is the minimum value of y=(x−1)2y=(x-1)^2?

Please select an answer first.

Correct answer: B

The correct answer is 0.

  1. Identify the quadratic structure: Determine the coefficients, factor form, graph features, roots, or discriminant requested.
  2. Apply a quadratic method: A square is never negative, and it is zero when x = 1, so the minimum value is 0.
  3. Check the result: The correct choice is 0.

A square is never negative, and it is zero when x = 1, so the minimum value is 0.

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