How to Find the Vertex and Axis of Symmetry in Absolute Value Functions

TL;DR

To find the vertex of an absolute value function, set the inside part equal to zero, which gives the x-coordinate. Then, substitute this x-coordinate back into the function to find the y-coordinate. The axis of symmetry is the line x equals the x-coordinate of the vertex.

Transcript

in this video we're going to talk about how to find the vertex and the axis of symmetry for an absolute value function so first we're going to set the inside part equal to zero and we'll solve for x we'll get if you add two to both sides you get X is equal to two so this is the axis of symmetry and it's also the x coordinate of the vertex to find t... Read More

Key Insights

• 😫 The axis of symmetry is found by setting the inside part of the absolute value function equal to zero.
• ☺️ The x-coordinate of the vertex is the same as the axis of symmetry.
• ❣️ The y-coordinate of the vertex is obtained by substituting the x-coordinate into the function.
• 📈 A positive sign in front of the absolute value indicates an upward-opening graph, while a negative sign indicates a downward-opening graph.
• 📈 The vertex and axis of symmetry can be used to graph the absolute value function.
• 🇭🇰 The general equation for finding the vertex and axis of symmetry is |x - H| + K, where the vertex is (H, K) and the axis of symmetry is x = H.
• ❓ Knowledge of finding the vertex and axis of symmetry in absolute value functions is helpful for studying this topic further.

Questions & Answers

Q: How do you find the axis of symmetry for an absolute value function?

To find the axis of symmetry, set the inside part of the absolute value function equal to zero and solve for x. The resulting x-value will be the axis of symmetry.

Q: How do you find the vertex of an absolute value function?

The x-coordinate of the vertex is the same as the axis of symmetry. To find the y-coordinate, substitute the x-coordinate back into the function and simplify.

Q: How does the sign in front of the absolute value function affect the graph?

A positive sign indicates the graph opens upward, while a negative sign indicates the graph opens downward.

Q: Is there a general equation to find the vertex and axis of symmetry?

Yes, if you have an absolute value function in the form of |x - H| + K, the vertex will be (H, K) and the axis of symmetry will be x = H.

Summary & Key Takeaways

• To find the axis of symmetry and vertex of an absolute value function, set the inside part equal to zero and solve for x. The axis of symmetry will be the x-coordinate of the vertex.

• To find the y-coordinate of the vertex, plug the x-coordinate back into the formula and simplify.

• The graph of an absolute value function with a positive sign opens upward, while a negative sign indicates the graph opens downward.