Basic Algebra Parent Functions
Description/Explanation/Highlights
Video Description
This video explains the linear and quadratic parent functions and their characteristics.
Steps and Key Points to Remember
To recognize and work with the linear and quadratic parent functions, follow these steps:
- The parent function of the linear family of functions in \(y=x\).
- The linear parent, like all functions in the linear family, will make a line when graphed.
- The linear parent (\(y=x\)) has a slope of positive 1 and intersects the x- and y-axis at (0, 0). \(y=-x\) is not a parent function as it will have a negative slope of 1.
- \(y=x+3\) is also not a parent function because even though it still has a slope of positive 1, it will not pass through the origin at (0, 0) but will instead be moved up three and pass through (0, 3).
- \(y=x^2\) is the parent function of the quadratic function family.
- The quadratic parent, like all quadratics, will form a U-shape called a parabola when graphed.
- The parent opens up and has a vertex at (0, 0) and reflects across the y-axis.
- The y-values of the points in the parabola can be found by squaring the x-values.
Here are some key points to keep in mind when working with linear and quadratic parent functions and their characteristics.
- \(y=x\) is the linear parent function.
- The linear parent graphs a line with a slope of one and a y-intercept at the origin (0, 0).
- It is no longer the linear parent if the slope is changed to negative \(y=-x\).
- \(y=x^2\) is the quadratic parent function.
- The quadratic parent forms a parabola when graphed, opens upward, and has a vertex at the origin (0, 0).
Video Highlights
- 00:00 Introduction
- 00:20 \(y=x\) linear parent
- 01:32 Characteristics of the linear parent
- 03:07 \(y=x^2\) quadratic parent
- 05:03 Characteristics of the quadratic parent function
- 06:42 Conclusion
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