[
  {
    "Question": "What is the vertex form of a quadratic function?",
    "Answer": "A",
    "Explanation": "The vertex form of a quadratic function is given by the equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola.",
    "PictureURL": "",
    "OptionA": "y = a(x - h)² + k",
    "OptionB": "y = ax² + bx + c",
    "OptionC": "y = a(x + h)² + k",
    "OptionD": "y = ax² - bx + c",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Understanding Vertex Form",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/vertex-form"
  },
  {
    "Question": "What is the axis of symmetry for the quadratic function y = 2x² + 4x + 1?",
    "Answer": "B",
    "Explanation": "The axis of symmetry can be found using the formula x = -b/(2a). Here, a = 2 and b = 4, so x = -4/(2*2) = -1.",
    "PictureURL": "",
    "OptionA": "-2",
    "OptionB": "-1",
    "OptionC": "0",
    "OptionD": "1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding Axis of Symmetry",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/axis-of-symmetry"
  },
  {
    "Question": "Which of the following points is the vertex of the parabola represented by the equation y = -3(x + 2)² + 5?",
    "Answer": "C",
    "Explanation": "In the vertex form y = a(x - h)² + k, the vertex is at (h, k). Here, h = -2 and k = 5, so the vertex is (-2, 5).",
    "PictureURL": "",
    "OptionA": "(2, -5)",
    "OptionB": "(-2, -5)",
    "OptionC": "(-2, 5)",
    "OptionD": "(5, -2)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Identifying the Vertex",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/vertex-identification"
  },
  {
    "Question": "What is the direction of the parabola for the function y = -x² + 4?",
    "Answer": "A",
    "Explanation": "The coefficient of x² is negative (-1), which means the parabola opens downwards.",
    "PictureURL": "",
    "OptionA": "Downwards",
    "OptionB": "Upwards",
    "OptionC": "Left",
    "OptionD": "Right",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Direction of the Parabola",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/parabola-direction"
  },
  {
    "Question": "What is the y-intercept of the quadratic function y = x² - 3x + 2?",
    "Answer": "B",
    "Explanation": "The y-intercept occurs when x = 0. Plugging in 0 gives y = 0² - 3(0) + 2 = 2.",
    "PictureURL": "",
    "OptionA": "0",
    "OptionB": "2",
    "OptionC": "3",
    "OptionD": "1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Y-Intercept",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/y-intercept"
  },
  {
    "Question": "Which of the following represents the axis of symmetry for the quadratic function y = 4x² - 8x + 3?",
    "Answer": "A",
    "Explanation": "Using the formula x = -b/(2a), where a = 4 and b = -8, we find x = 8/(2*4) = 1.",
    "PictureURL": "",
    "OptionA": "1",
    "OptionB": "2",
    "OptionC": "0",
    "OptionD": "-1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Axis of Symmetry Calculation",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/axis-of-symmetry-calculation"
  },
  {
    "Question": "What is the minimum value of the function y = 2(x - 3)² + 1?",
    "Answer": "C",
    "Explanation": "Since the parabola opens upwards (a = 2 > 0), the minimum value is at the vertex, which is y = 1.",
    "PictureURL": "",
    "OptionA": "0",
    "OptionB": "2",
    "OptionC": "1",
    "OptionD": "3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding Minimum Value",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/minimum-value"
  },
  {
    "Question": "For the quadratic function y = x² + 6x + 8, what is the vertex?",
    "Answer": "B",
    "Explanation": "To find the vertex, use x = -b/(2a). Here, a = 1 and b = 6, so x = -6/2 = -3. Plugging x back gives y = 1.",
    "PictureURL": "",
    "OptionA": "(-3, 1)",
    "OptionB": "(-3, -1)",
    "OptionC": "(3, 1)",
    "OptionD": "(3, -1)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Vertex",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/vertex-calculation"
  },
  {
    "Question": "What is the effect of changing the value of 'a' in the vertex form y = a(x - h)² + k?",
    "Answer": "D",
    "Explanation": "Changing 'a' affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider.",
    "PictureURL": "",
    "OptionA": "Changes the vertex position",
    "OptionB": "Changes the axis of symmetry",
    "OptionC": "Changes the y-intercept",
    "OptionD": "Changes the width and direction",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Effect of 'a' in Vertex Form",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/effect-of-a"
  },
  {
    "Question": "What is the standard form of the quadratic function y = 2(x - 1)² + 3?",
    "Answer": "C",
    "Explanation": "To convert to standard form, expand the vertex form: y = 2(x² - 2x + 1) + 3 = 2x² - 4x + 5.",
    "PictureURL": "",
    "OptionA": "2x² + 4x + 5",
    "OptionB": "2x² - 2x + 3",
    "OptionC": "2x² - 4x + 5",
    "OptionD": "2x² + 2x + 3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Converting to Standard Form",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/standard-form"
  },
  {
    "Question": "What is the range of the function y = -2(x + 1)² + 4?",
    "Answer": "B",
    "Explanation": "Since the parabola opens downwards and the vertex is at (−1, 4), the range is y ≤ 4.",
    "PictureURL": "",
    "OptionA": "y ≥ 4",
    "OptionB": "y ≤ 4",
    "OptionC": "y = 4",
    "OptionD": "y < 4",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Range",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/range"
  },
  {
    "Question": "Which of the following equations represents a parabola that opens upwards?",
    "Answer": "A",
    "Explanation": "A parabola opens upwards when the coefficient of x² is positive. Here, a = 3, which is positive.",
    "PictureURL": "",
    "OptionA": "y = 3x² + 2x + 1",
    "OptionB": "y = -3x² + 2x + 1",
    "OptionC": "y = 0.5x² - 2x + 1",
    "OptionD": "y = -0.5x² + 2x + 1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Identifying Upward Opening Parabola",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/upward-opening"
  },
  {
    "Question": "What is the x-coordinate of the vertex for the function y = -x² + 6x - 8?",
    "Answer": "C",
    "Explanation": "Using the vertex formula x = -b/(2a), where a = -1 and b = 6, we find x = -6/(2*-1) = 3.",
    "PictureURL": "",
    "OptionA": "2",
    "OptionB": "4",
    "OptionC": "3",
    "OptionD": "6",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding X-Coordinate of Vertex",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/x-coordinate-vertex"
  },
  {
    "Question": "Which of the following is true about the roots of the quadratic equation y = x² - 4?",
    "Answer": "B",
    "Explanation": "The roots can be found by factoring: y = (x - 2)(x + 2) = 0, giving roots x = 2 and x = -2.",
    "PictureURL": "",
    "OptionA": "There are no real roots",
    "OptionB": "There are two real roots",
    "OptionC": "There is one real root",
    "OptionD": "There is one complex root",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Understanding Roots of Quadratic Equations",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/roots"
  },
  {
    "Question": "What is the formula to find the vertex of a parabola in standard form?",
    "Answer": "A",
    "Explanation": "The vertex of a parabola in standard form y = ax² + bx + c can be found using x = -b/(2a).",
    "PictureURL": "",
    "OptionA": "x = -b/(2a)",
    "OptionB": "x = b/(2a)",
    "OptionC": "x = a/(2b)",
    "OptionD": "x = -2b/a",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Quadratic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding Vertex Formula",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "/quadratic-functions/vertex-formula"
  }
]