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move at least one of the 5 guide points below to complete the graph of $y=(x-7)^2 - 8$. 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 $y=(x-7)^2-8$, the vertex is $(7, -8)$. The current blue vertex is at $(0,0)$, so we shift it right 7 units and down 8 units to $(7, -8)$.

Step2: Identify other key points

For the parent function $y=x^2$, when $x=1$, $y=1$; $x=2$, $y=4$. For $y=(x-7)^2-8$:

• When $x=6$: $y=(6-7)^2-8=1-8=-7$
• When $x=8$: $y=(8-7)^2-8=1-8=-7$
• When $x=5$: $y=(5-7)^2-8=4-8=-4$
• When $x=9$: $y=(9-7)^2-8=4-8=-4$

These correspond to the red points, so move the red points from $(-1,1), (1,1), (-2,4), (2,4)$ to $(6,-7), (8,-7), (5,-4), (9,-4)$ respectively.

Answer:

1. Move the blue vertex point from $(0,0)$ to $(7, -8)$.
2. Move the red point at $(-1,1)$ to $(6,-7)$.
3. Move the red point at $(1,1)$ to $(8,-7)$.
4. Move the red point at $(-2,4)$ to $(5,-4)$.
5. Move the red point at $(2,4)$ to $(9,-4)$.

The resulting graph will be the parabola $y=(x-7)^2-8$.