b Use that (x+2)^3 can be written as (x+2)(x+2)(x+2).
C
c Has the function changed in any way when you rewrote it?
A
aParent Function: y=x^3 Transformation: 2 steps left and 4 steps up.
B
b y=x^3+6x^2+12x+12
C
c It wouldn't.
Practice makes perfect
a This is a cubic function. Such a function can be described with the following general equation.
General Equation:& y=a(x-h)^3+k
Locator Point:& (h,k)
The locator point of a cubic function, describes its inflection point. This is where the function switches from a decreasing rate of change to an increasing rate of change. The parent function of all cubic functions is y=x^3 and this graph has its locator point at the origin.
The given graph adds 2 to the input and 4 to the output of the parent function. Let's rewrite the given function so that it matches the graphing form of a cubic function exactly. This will allow us to find its locator point.
Function:& y=(x-(-2))^3+4
Locator Point:& (-2,4)
If we compare the locator point of the given function and the parent function, we see that this is a translation of the parent function by 2 units to the left and 4 units up.
b Since powers describes repeated multiplication, (x+2)^3 can be written as the following product.
(x+2)(x+2)(x+2)
We can multiply the first pair of parentheses together, and then multiply the result with the last parentheses to rewrite the equation without parentheses.
c In Part B we rewrote the original equation. We didn't change it. It's still the same function, so there's no reason to think the graphs would look different. If we graph both of them, they would overlap
