Unit 1, Day 1: Parent Functions
October 27, 2025
Today's Goal
I will be able to spot the three main "starter" graphs, know their simple equations, and draw them using the Desmos calculator website.
Warm-Up
In math, a parent function is like the original, basic model for a whole family of graphs.
All the other graphs in the family are just slightly different versions of their parent. Today, we'll meet the three most important parents.
I Do: The Linear Parent
The first parent is Linear (which just means a perfectly straight line). Its equation is super simple:
$f(x) = x$
- Its graph is a straight line that cuts the graph in half.
- It goes right through the origin (the center point where the lines cross).
- See it for yourself: Go to desmos.com and type
y=x.
We Do: The Quadratic Parent
Next is the Quadratic parent. ("Quadratic" is a fancy word for graphs where the $x$ is squared, or $x^2$.)
$f(x) = x^2$
- Its graph is a "U-shape" called a parabola.
- The bottom of the "U" is right at the origin (the center).
- Let's graph it together: In a new line in Desmos, type
$y=x^2$.
You Do: The Exponential Parent
Finally, we have the Exponential parent. ("Exponential" means the letter $x$ is up in the exponent spot.)
$f(x) = 2^x$
Your turn:
- Graph
$y=2^x$in Desmos. - How would you describe its shape? It's like a ramp that gets super steep!
Independent Practice
Complete the level that feels right for you. Challenge yourself!
Green Level
Remembering
Match the name to its equation:
1. Linear
2. Quadratic
3. Exponential
A) $y=x^2$
B) $y=2^x$
C) $y=x$
Yellow Level
Applying
Which parent graph on Desmos...
- ...is a curved U-shape?
- ...is a straight line?
- ...starts flat and gets steep fast?
Red Level
Analyzing
Answer the following:
- Which shape best models a thrown basketball's path?
- What point do all three parent graphs have in common?
Exit Ticket
On a separate piece of paper, answer the following before you leave.
Write the equation for the quadratic (U-shape) parent.
Draw a quick sketch of the linear (straight line) parent.
Imagine money in a savings account growing with interest. Which graph shape would that look like? (Linear, Quadratic, or Exponential?)