Home > A2C > Chapter 6 > Lesson 6.2.2 > Problem6-80

6-80.

Consider the equation $y = \left(x + 6\right)^{2} − 7$. .

1. Explain completely how to get a good sketch of the graph of $y = \left(x + 6\right)^{2} − 7$.

Graph a regular $y = x^{2}$, but place its vertex at (−6, −7).

2. Explain how to change the original graph to represent the graph of $y = \left(x + 6\right)^{2} + 2$.

It would move vertically upwards.

3. Given the original graph, how can you get the graph of $y = | ( x + 6 ) ^ { 2 } - 7$?

Remember the meaning of absolute value.

4. Restrict the domain of the original parabola to $x ≥ −6$ and graph its inverse function.

Remember how to find the inverse of a function.

5. What would be the equation for the inverse function if you restricted the domain to $x ≥ −6$?

See part (d).

Use the eTool below to explore the graphs needed to solve the parts of the problem.
Click the link to the right for full version. 6-80 HW eTool