Question

move at least one of the 5 guide points below to complete the graph of $y=(x - 6)^2 - 8$. 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 vertex of target function

The vertex form of a parabola is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $y=(x-6)^2-8$, $h=6$, $k=-8$, so vertex is $(6,-8)$.

Step2: Shift blue vertex point

Move the blue vertex point from $(0,0)$ to $(6,-8)$.

Step3: Find points for red guide points

For the parent function $y=x^2$, points are $(1,1), (-1,1), (2,4), (-2,4)$. For $y=(x-6)^2-8$:

• When $x=6+1=7$, $y=(7-6)^2-8=1-8=-7$
• When $x=6-1=5$, $y=(5-6)^2-8=1-8=-7$
• When $x=6+2=8$, $y=(8-6)^2-8=4-8=-4$
• When $x=6-2=4$, $y=(4-6)^2-8=4-8=-4$

Step4: Move red guide points

Move the red points from $(1,1)$ to $(7,-7)$, $(-1,1)$ to $(5,-7)$, $(2,4)$ to $(8,-4)$, $(-2,4)$ to $(4,-4)$.

Answer:

1. Move the blue vertex point to $(6, -8)$.
2. Move the red point at $(1,1)$ to $(7, -7)$.
3. Move the red point at $(-1,1)$ to $(5, -7)$.
4. Move the red point at $(2,4)$ to $(8, -4)$.
5. Move the red point at $(-2,4)$ to $(4, -4)$.

This will complete the graph of $y=(x-6)^2-8$.