Vertex

Definition

The vertex is a key point on a graph or function that represents the maximum or minimum value of the function. It is the point where the graph changes direction, either from increasing to decreasing or vice versa.

5 Must Know Facts For Your Next Test

1. The vertex of a quadratic function is the point where the graph changes direction, either from increasing to decreasing or vice versa.
2. For an absolute value function, the vertex represents the point where the function changes direction and is the point of the minimum or maximum value.
3. The vertex of an ellipse is the point on the graph that represents the maximum or minimum value of the function.
4. In a system of nonlinear equations, the vertex represents the point where the graphs of the equations intersect, which is the solution to the system.
5. The vertex of a parabola is the point where the graph changes direction and is the point of the maximum or minimum value of the function.

Review Questions

• Explain the significance of the vertex in the context of quadratic functions.
  • The vertex of a quadratic function is the point where the graph changes direction, either from increasing to decreasing or vice versa. This point represents the maximum or minimum value of the function, and it is the point where the graph intersects the axis of symmetry. The vertex is an important feature of quadratic functions, as it provides information about the function's behavior and can be used to analyze and solve various problems related to quadratic equations.
• Describe how the vertex relates to the graph of an absolute value function.
  • For an absolute value function, the vertex represents the point where the function changes direction, either from increasing to decreasing or vice versa. This point is the minimum or maximum value of the function, and it is the point where the graph intersects the x-axis. The vertex is a crucial feature of absolute value functions, as it provides information about the function's behavior and can be used to analyze and solve various problems related to absolute value equations.
• Analyze the role of the vertex in the context of systems of nonlinear equations and inequalities involving two variables.
  • In a system of nonlinear equations, the vertex represents the point where the graphs of the equations intersect, which is the solution to the system. The vertex is the point of intersection that satisfies both equations simultaneously. Additionally, in a system of nonlinear inequalities, the vertex represents the point where the boundaries of the inequalities intersect, which is the region of the solution set. The vertex is a critical feature in understanding and solving systems of nonlinear equations and inequalities, as it provides the key information needed to determine the solution or solution set.

Related terms

Axis of Symmetry: The axis of symmetry is a line that passes through the vertex of a parabolic function, dividing the graph into two equal halves.

Parabola: A parabola is a U-shaped curve that is the graph of a quadratic function, and the vertex represents the point of maximum or minimum value on the parabola.

Absolute Value Function: The vertex of an absolute value function represents the point where the function changes direction, either from increasing to decreasing or vice versa.