Question

What is the cubic function for the transformation : flip over x axis, move left 3 and up 5

Answer 1

Cubic Function Form:

y=$ax^{3} +bx^{2} +cx+d$

However here we only need ax^3 and +d

ax^3 makes the graph wider or skinnier or reflects it if negative.

So the first coefficient will be negative since we want to reflect it along the x axis

To move left three we will have to add 3 to the ax^3 giving us something like (x+3)^3

To move up 5 we set our y intercept (the +d part) to d=5.

Combing everything together gives us (x+3)^3+5