Quadratic Functions Essentials

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The quiz Quadratic Functions Essentials contains 15 multiple choice questions with one correct answer.

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Author: Justice

This quiz checks your understanding of quadratic functions, including their definitions, graph properties, discriminant, roots, vertex, and different forms. Expect questions on recognizing quadratics, computing key parameters, and interpreting common mistakes.

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1 Which of the following is a quadratic function?

A f(x) = 3x + 2 B f(x) = 2x² - 5x + 1 C f(x) = x³ - x² + 4 D f(x) = √x + 7

2 The vertex of the parabola y = 2(x − 3)² + 5 has coordinates:

A (3, 5) B (-3, -5) C (-3, 5) D (3, -5)

3 For the function f(x) = −x² + 4x − 3, the arms of the parabola are directed:

A Downward, because a = −1 B Upward, because a = 1 C Downward, because b = 4 D Upward, because the constant term is negative

4 The discriminant Δ of the function f(x) = x² − 6x + 9 equals:

A Δ = 0 B Δ = −36 C Δ = 36 D Δ = 9

5 For f(x) = 3x² − 12x + 7, the function attains its minimum value when:

A x = 7 B x = 2 C x = −2 D x = 4

6 The roots of the function f(x) = x² − 5x + 6 are:

A x = −2 and x = −3 B x = 1 and x = 6 C x = 0 and x = 5 D x = 2 and x = 3

7 The vertex of the parabola y = 2x² + 8x − 3 is located at:

A W = (−2, 11) B W = (2, −11) C W = (−2, −11) D W = (2, 11)

8 The canonical form of f(x) = x² − 4x + 7 is:

A f(x) = (x + 2)² + 7 B f(x) = (x − 2)² + 3 C f(x) = (x + 2)² − 3 D f(x) = (x − 2)² − 7

9 The factored (product) form of f(x) = 2x² − 10x + 12 is:

A f(x) = 2(x + 2)(x + 3) B f(x) = 2(x + 1)(x − 6) C f(x) = 2(x − 2)(x − 3) D f(x) = 2(x − 1)(x − 6)

10 For f(x) = −x² + 3x + 10, the value of the function at x = 4 is:

A f(4) = 10 B f(4) = 0 C f(4) = 6 D f(4) = −2

11 Which statement about quadratic functions is true when a > 0 in f(x) = ax² + bx + c?

A The function never intersects the y-axis B The function has a maximum value at its vertex C The function has a minimum value at its vertex D The function always has two distinct real roots

12 Which statement about the number of real zeros of a quadratic function is correct?

A If Δ = 0, there are no real zeros at all B If Δ > 0, there are two different real zeros C Every quadratic has two different real zeros D If Δ < 0, there are two equal real zeros

13 In the general form f(x) = ax² + bx + c, the coefficient c represents:

A The slope of the axis of symmetry B The x-coordinate of the vertex C The y-coordinate of the vertex D The y-intercept of the graph

14 A parabola opens downward (a < 0) and its vertex lies below the x-axis (y_w < 0). Which is true?

A It has exactly one real zero B It has two distinct real zeros C It has no real zeros D It always passes through the origin

15 Kasia computes Δ for f(x) = x² − 4x + 4 as Δ = 16 by using Δ = b² only. What is the correct discriminant?

A Δ = 16, because c does not affect Δ B Δ = −16, because a is positive C Δ = 4, because 16 − 12 = 4 D Δ = 0, because 16 − 16 = 0

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How many questions does the quiz Quadratic Functions Essentials have?

The quiz Quadratic Functions Essentials contains 15 multiple choice questions with one correct answer.

Is the quiz Quadratic Functions Essentials free?

Yes, all quizzes on CramZap are completely free. You can take as many quizzes as you want without any charges.

How can I create my own quiz?

Upload a PDF file on the homepage and our AI will automatically generate quiz questions. After generation you can edit the questions and answers in your quiz dashboard.

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