Function Basics Review Quiz

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
Learn about Our Editorial Process
| By Nathan Kunkel
N
Nathan Kunkel
Community Contributor
Quizzes Created: 2 | Total Attempts: 634
Questions: 5 | Attempts: 81

SettingsSettingsSettings
Function Basics Review Quiz - Quiz

Just a short 5 question quiz review basics of translating functions.


Questions and Answers
  • 1. 

    Identify the vertex and y-intercept of the graph of the function y = 3(x + 2)2 - 5.

    • A.

      Vertex: (-2, -5) y-intercept: 7

    • B.

      Vertex: (2, 5) y-intercept: 12

    • C.

      Vertex: (2, -5) y-intercept: 7

    • D.

      Vertex: (-2, 5) y-intercept: 1

    Correct Answer
    A. Vertex: (-2, -5) y-intercept: 7
    Explanation
    The vertex of a quadratic function in the form y = a(x - h)^2 + k is given by (h, k). In this case, the equation is y = 3(x + 2)^2 - 5, so the vertex is (-2, -5). The y-intercept is the value of y when x = 0. Plugging in x = 0 into the equation, we get y = 3(0 + 2)^2 - 5 = 3(4) - 5 = 12 - 5 = 7. Therefore, the y-intercept is 7.

    Rate this question:

  • 2. 

    Write the equation of the parabola in vertex form. vertex: (-2, 4), point: (2, 84)

    • A.

      Y = 5(x - 2)2 + 4

    • B.

      Y = 84(x + 2)2 - 4

    • C.

      Y = 5(x + 2)2+4

    • D.

      Y = 2(x - 2)2 + 4

    Correct Answer
    C. Y = 5(x + 2)2+4
    Explanation
    The equation of a parabola in vertex form is given by y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, the vertex is (-2, 4), so the equation should be of the form y = a(x + 2)^2 + 4. Since the given equation y = 5(x + 2)^2 + 4 matches this form, it is the correct answer.

    Rate this question:

  • 3. 

    Which quadratic function does the graph represent?

    • A.

      F(x) = -x2 + 6x + 7

    • B.

      F(x) = x2 + 6x - 7

    • C.

      F(x) = -x2 + 6x - 7

    • D.

      F(x) = -x2 - 6x - 7

    Correct Answer
    C. F(x) = -x2 + 6x - 7
    Explanation
    The given quadratic function is f(x) = -x^2 + 6x - 7. This can be determined by analyzing the coefficients of the quadratic equation. The quadratic term has a negative coefficient, indicating that the graph opens downwards. The linear term has a positive coefficient, indicating that the graph has a positive slope. The constant term is negative, indicating that the graph intersects the y-axis below the origin. Therefore, the correct answer is f(x) = -x^2 + 6x - 7.

    Rate this question:

  • 4. 

    Use vertex form to write the equation of the parabola.

    • A.

      Y = 2(x - 3)2 - 2

    • B.

      Y = 2(x + 3)2 - 2

    • C.

      Y = 2(x + 3)2 + 2

    • D.

      Y = (x - 3)2 - 2

    Correct Answer
    A. Y = 2(x - 3)2 - 2
    Explanation
    The given equation is in the vertex form of a parabola, which is y = a(x - h)^2 + k. In this equation, the vertex of the parabola is represented by the point (h, k).

    Comparing the given equation y = 2(x - 3)^2 - 2 with the vertex form, we can see that the vertex of the parabola is at the point (3, -2). The coefficient "2" in front of the (x - 3)^2 term indicates that the parabola is stretched vertically. Since the coefficient is positive, the parabola opens upward. Therefore, the equation y = 2(x - 3)^2 - 2 represents a parabola with its vertex at (3, -2), opening upward, and stretched vertically.

    Rate this question:

  • 5. 

    The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form. 

    • A.

      G(x) = 7(x + 3)2

    • B.

      G(x) = -3(x - 7)2

    • C.

      G(x) = -3(x + 7)2

    • D.

      G(x) = 3(x - 7)2

    Correct Answer
    B. G(x) = -3(x - 7)2
    Explanation
    The parent function f(x) = x^2 is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. The equation g(x) = -3(x - 7)^2 represents this transformation. The negative sign indicates the reflection across the x-axis, the coefficient -3 represents the vertical stretch, and the (x - 7)^2 term represents the translation right 7 units. Thus, the correct answer is g(x) = -3(x - 7)^2.

    Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Apr 11, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Apr 06, 2020
    Quiz Created by
    Nathan Kunkel
Back to Top Back to top
Advertisement
×

Wait!
Here's an interesting quiz for you.

We have other quizzes matching your interest.