Question

move at least one of the 5 guide points below to complete the graph of ( y = (x - 6)^2 + 3 ). moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x - axis.

Explanation:

Step1: Identify parent function

Parent function: $y=x^2$, with key points $(0,0),\ (1,1),\ (-1,1),\ (2,4),\ (-2,4)$

Step2: Apply horizontal shift

Shift right 6 units: replace $x$ with $x-6$. New points: $(0+6,0)=(6,0),\ (1+6,1)=(7,1),\ (-1+6,1)=(5,1),\ (2+6,4)=(8,4),\ (-2+6,4)=(4,4)$

Step3: Apply vertical shift

Shift up 3 units: add 3 to $y$-values.
New points:
$(6,0+3)=(6,3)$
$(7,1+3)=(7,4)$
$(5,1+3)=(5,4)$
$(8,4+3)=(8,7)$
$(4,4+3)=(4,7)$

Answer:

The key points for $y=(x-6)^2+3$ are:

1. Vertex: $(6, 3)$
2. Point 1: $(5, 4)$
3. Point 2: $(7, 4)$
4. Point 3: $(4, 7)$
5. Point 4: $(8, 7)$