Based on the passage, which of the following statements about the graph of a qua

Practice Questions

Q1
Based on the passage, which of the following statements about the graph of a quadratic function is true?
  1. It can have at most one x-intercept.
  2. It is always increasing.
  3. It is a parabola that opens upwards or downwards.
  4. It has no maximum or minimum points.

Questions & Step-by-Step Solutions

Based on the passage, which of the following statements about the graph of a quadratic function is true?
  • Step 1: Understand that a quadratic function is a type of mathematical function that can be written in the form of ax^2 + bx + c, where a, b, and c are numbers.
  • Step 2: Recognize that the graph of a quadratic function is called a parabola.
  • Step 3: Identify that the direction in which the parabola opens (upwards or downwards) depends on the value of 'a' (the coefficient of the x^2 term).
  • Step 4: If 'a' is positive (greater than 0), the parabola opens upwards. If 'a' is negative (less than 0), the parabola opens downwards.
  • Step 5: Use this information to determine which statement about the graph of a quadratic function is true based on the passage.
  • Quadratic Functions – Quadratic functions are polynomial functions of degree two, typically represented in the form f(x) = ax^2 + bx + c, where the graph is a parabola.
  • Parabola Orientation – The orientation of a parabola (opening upwards or downwards) is determined by the sign of the coefficient 'a' in the quadratic function.
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