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Parent Graphs

Master parent graphs with interactive lessons and practice problems! Designed for students like you!

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Parent Graphs

Study Guide

Key Definition

A parent graph is the graph of a simple function like $y = mx + b$ or $y = x^2$.

Important Notes

Transformations can change the graph's position and shape.
Parent graphs include linear, quadratic, and cubic functions.
Understanding parent graphs is crucial for mastering transformations.
Each function type has unique characteristics and shapes.
Practice identifying different parent graphs by their equations.

Mathematical Notation

$y = mx + b$ represents a linear function

$x^2$ represents a quadratic function

$\sqrt{x}$ represents a square root function

$\sin(x)$ is the sine function

$\log(x)$ is the logarithmic function

Remember to use proper notation when solving problems

Why It Works

Parent graphs provide a foundation for understanding how transformations affect the shape and position of graphs.

Remember

Knowing the basic shape of each parent graph helps in predicting transformations.

Quick Reference

Linear Function:$y = mx + b$

Quadratic Function:$y = x^2$

Cubic Function:$y = x^3$

Square Root Function:$y = \sqrt{x}$

Exponential Function:$y = a^x$

Understanding Parent Graphs

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Parent graphs are the simplest forms of functions before any transformations. For example, the parent graph of a linear function is y = mx + b, which appears as a straight line with slope m and intercept b. The parent graph of a quadratic function is y = x^2, a U-shaped parabola symmetric about the y-axis. Recognizing these basic shapes helps you understand how lines and parabolas behave.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following equations represents a linear function?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A skateboarder jumps off a ramp. His height $h$ in meters can be modeled by $h = -5t^2 + 10t + 1$, where $t$ is time in seconds. What is the maximum height he reaches?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine if the function $f(x) = x^2 - 4x + 4$ is a transformation of the parent graph $y = x^2$.

Challenge Quiz

Single Choice Quiz

Advanced

Which function represents an exponential growth? $y = 2^x$ or $y = x^2$

Recap

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Review key concepts and takeaways