Graph the polynomial P(x)=-(x+2)^{3}+27, showing clearly all x- and y-

vazelinahS

vazelinahS

Answered question

2021-08-08

Graph the polynomial P(x)=(x+2)3+27, showing clearly all x- and y- intercepts.

Answer & Explanation

doplovif

doplovif

Skilled2021-08-09Added 71 answers

Work as shown below, follow the steps:
P(x)=(x+2)3+27
Graph this function by using transformations of the graph of the parent function f(x)=x3:
The function P can be written in terms of the parent function f as:
P(x)=f(x+2)+27
So the transformations we have to apply to the graph of f to get the graph of P are:
-Horizontal translation 2 units left.
-Reflection through the x-axis.
Vertical translation 27 units upward.
See the graphs of these two functions in the following picture:

Answer: The transformations we have to apply to the graph of f to get the graph of P are: horizontal translation 2 units left, reflection throught the x-axis, and vertical translation 27 units upward. Intercepts: x=1 and y=19

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