Function Transformation Math Example 1

Solution

1. 1
   Write in standard form $y = a\cdot f(b(x-h))+k$: here $a=2$, $b=1$, $h=3$, $k=1$.
2. 2
   Horizontal shift: $h=3$ shifts the parabola $3$ units to the right (vertex moves from $(0,0)$ to $(3,0)$).
3. 3
   Vertical stretch: $a=2$ stretches vertically by factor $2$ (makes parabola narrower). Vertical shift: $k=1$ shifts the entire graph $1$ unit up. Final vertex: $(3, 1)$.