How To Find The Domain and Range of a Quadratic Function

TL;DR

Learn how to find the domain and range of quadratic functions by analyzing their graphs and understanding transformations.

Transcript

in this video we're going to talk about how to find the domain and range of a quadratic function so let's start with the parent function y is equal to x squared what is the domain and range of that function it really helps if you can draw the graph if you can see the graph it's very easy to determine the domain and range now when finding the domain... Read More

Key Insights

• 🧡 Quadratic functions have a domain of all real numbers and a range that depends on the direction of the opening of the graph.
• ✖️ Multiplying a quadratic function by a negative sign reflects it over the x-axis, changing the range.
• 🧡 Transformations of quadratic functions affect the vertex position but not the domain, while the range may shift accordingly.
• 🧡 Factoring quadratic functions helps in identifying the vertex and finding the domain and range.
• ☺️ The vertex formula can be used to find the x-coordinate of the vertex, which determines the domain and range.

Summary & Key Takeaways

• Quadratic functions have a domain of all real numbers and a range that goes from zero to positive infinity.

• When the quadratic function is multiplied by a negative sign, it reflects over the x-axis, resulting in a range from negative infinity to zero.

• Transformation of quadratic functions can change the vertex, but the domain remains the same while the range varies depending on the shift.

• Quadratic functions can also be written in standard form, and the domain and range can be found using the vertex formula.

• Factoring quadratic functions helps in finding the x-intercepts, which allows us to determine the vertex and the corresponding range.