Question

move at least one of the 5 guide points below to complete the graph of ( y = (x - 6)^2 ). 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.
reset
reflect over x - axis

Explanation:

Step1: Identify the vertex form

The function is \( y=(x - 6)^2 \), which is a parabola in vertex form \( y = a(x - h)^2 + k \), where the vertex is \( (h,k)=(6,0) \).

Step2: Analyze the current graph

The current blue point (vertex) is at \( (0,0) \), and we need to shift it to \( (6,0) \). Also, the red points should follow the parabola \( y=(x - 6)^2 \). For example, when \( x = 5 \), \( y=(5 - 6)^2 = 1 \); when \( x = 7 \), \( y=(7 - 6)^2 = 1 \); when \( x = 4 \), \( y=(4 - 6)^2 = 4 \); when \( x = 8 \), \( y=(8 - 6)^2 = 4 \).

Step3: Move the blue point

Move the blue vertex point from \( (0,0) \) to \( (6,0) \). Then adjust the red points: for \( x = 5 \), move the red point to \( (5,1) \); for \( x = 7 \), move to \( (7,1) \); for \( x = 4 \), move to \( (4,4) \); for \( x = 8 \), move to \( (8,4) \). This will form the graph of \( y=(x - 6)^2 \).

Answer:

Move the blue vertex point to \( (6,0) \) and adjust the red points to lie on \( y=(x - 6)^2 \) (e.g., \( (5,1) \), \( (7,1) \), \( (4,4) \), \( (8,4) \)) to complete the graph.