How do I interpret the graph of a quadratic function?

Question

James Allen · Accepted Answer

For any graph, we are interested in minimums, maximums, y-intercept, x-intercepts, multiplicity of roots, symmetry, asymptotes, concavity, and end behaviour at #-oo# and #oo#.  When you start calculus, you are also interested in inflection points. Regarding quadratics:

Theodore Amidon · Answer

undefined To interpret the graph of a quadratic function, consider the following key points:

1. Vertex: The vertex represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards, respectively. It is the turning point of the graph.

2. Axis of Symmetry: The axis of symmetry is a vertical line passing through the vertex that divides the parabola into two symmetrical halves.

3. Roots (or Zeros): The roots of the quadratic function are the points where the graph intersects the x-axis. These are the solutions to the quadratic equation f(x) = 0.

4. Direction of Opening: The direction in which the parabola opens is determined by the coefficient of the squared term (a) in the quadratic function. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

5. y-intercept: The y-intercept is the point where the graph intersects the y-axis. It can be found by substituting x = 0 into the quadratic function.

By considering these aspects of the graph, you can interpret the behavior and characteristics of the quadratic function visually.