Transformers: Shifty y’s

Learning Focus

Describe vertical and horizontal shifts of $y=x^2$ and read the vertex from the equation.

Big idea

$y=(x-h)^2+k$

• $h$ shifts horizontally: $x-h$ moves right $h$ (so $x+4$ moves left 4).
• $k$ shifts vertically: up if positive, down if negative.
• Vertex $(h,k)$; axis of symmetry $x=h$.

Worked example

$y=(x+2)^2-5$: $h=-2$, $k=-5$. Vertex $(-2,-5)$, axis $x=-2$, opens up so the minimum value is $-5$.

Takeaways

• Inside the square the sign is opposite to the direction of motion.
• Outside the square the sign matches the direction of motion.
• Shifts do not change the shape.