Shifts & Stretches

Move any graph around

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $f(x) + k$: up by $k$. $\;f(x - h)$: right by $h$, which is the opposite of what the sign suggests.
• $a \cdot f(x)$: vertical stretch by $a$, and a flip if $a < 0$.
• $y = a(x - h)^2 + k$ has its vertex at $(h, k)$.

Steps

1. Lifting a graph
2. Predict
3. Inside moves sideways
4. Land on the star
5. Stretch and flip
6. Match the curve
7. Shift left
8. Two moves