Private: CAIE Alevel Pure Maths 1 (AS)

Quadratic Graphs

  • Represent the solutions to a quadratic equation (an equation in the form of ax^2 + bx + c = 0)
  • Take the form of a parabolic shape
  • Have a vertex which is either a maximum or minimum point, depending on the sign of “a” in the equation
  • The x-coordinate of the vertex can be found using the formula x = -b / 2a, and the y-coordinate can be found by substituting this value into the equation

Using Quadratic Graphs

  • To determine the maximum or minimum value of the quadratic function represented by the graph
  • To find the x-intercepts (the points where the graph crosses the x-axis) which correspond to the solutions to the quadratic equation
  • To find the y-intercept (the point where the graph crosses the y-axis) which is the value of the quadratic function when x = 0
  • To model and analyze real-world situations that can be represented by a quadratic function, such as the trajectory of a projectile or the relationship between supply and demand.

Drawing Quadratic Graphs

  1. Plot several points along the graph using the quadratic equation
  2. Connect the plotted points to form a smooth curve
  3. Identify the vertex of the graph by finding the highest or lowest point, depending on the equation
  4. Determine the direction of the graph (whether it opens upwards or downwards) based on the sign of the coefficient “a in the equation
  5. Locate the x-intercepts, if any, by finding the points where the graph crosses the x-axis
  6. Determine the y-intercept by finding the point where the graph crosses the y-axis
  7. Use the information to sketch the final graph and label all important points, including the vertex and intercepts.
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