Question

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Step 1: Start with the equation f(x) x2. Write the equation for the graph of g(x) that has been
reflected, or flipped, over the x-axis. (2 points)
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has
also been shifted down 4 units. (2 points)
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has
also been shifted left 1 unit. (2 points)

Answer 1

`g(x)=-(x+1)^2-4`.

Explanation:

The parent function is

`f(x)=x^2`

Step 1: Start with the equation
`f(x)=x^2`. Write the equation for the graph of g(x) that has been

reflected, or flipped, over the x-axis.

`f_1(x)=-f(x)`

`f_1(x)=-x^2`

Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has

also been shifted down 4 units.

`f_2(x)=f_1(x)-4`

`f_2(x)=-x^2-4`

Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has

also been shifted left 1 unit.

`g(x)=f_2(x+1)`

`g(x)=-(x+1)^2-4`

Therefore, the required equation is
`g(x)=-(x+1)^2-4`.