Question

Describe how to transform the graph of f(x)=x2 to obtain the graph of the related function g(x)=−2(x+1)2+1. Then draw the graph of g(x).

Answer 1

• y=x²

First tranfer x to 1 units left .

• y=(x+1)²

Multiply by 2

• y=2(x+1)²

Flip the parabola (turn a negative)

• y=-2(x+1)²

Transfer y 1 units up

• y=-2(x+1)²+1

Answer 2

to go from y=x² which has a minimum vertex at (0,0), you must shift the vertex one unit to the left and then one unit up to get a maximum vertex at (-1,1)

you can then plot points that can be created from an x-y table; such as (1,-7), (-1,1), (2,17), (-2,-1), etc

Explanation: