Graph the polynomial by transforming an appropriate graph of the

mattgondek4

mattgondek4

Answered question

2021-08-08

Graph the polynomial by transforming an appropriate graph of the form y=xn. Show clearly all x- and y-intercepts.P(x)=2(x+1)432

Answer & Explanation

rogreenhoxa8

rogreenhoxa8

Skilled2021-08-09Added 109 answers

The parent function of P(x)=2(x+1)432 is y=x4, which passes through the points (2,16),(1,1),(0,0),(1,1),(2,16).
P(x)=2(x+1)432 is the graph of y=x4 vertically stratched by a factor of 2 and then translated left 1 unit and down 32 units. Vertically stretching the points on y=x4 by a factor of 2 gives the points (2,32),(1,2),(0,0),(1,2),(2,32). Translating these points left 1 unit and down 16 units then gives the points (3,0),(2,30),(1,32),(0,30),(1,0)
The x-intercept of P(x) is when P(x)=0, we which know is at the points (3,0),(1,0). The y-intercept is when x=0 which we already know is at the point (0,30). Plot the points and then connect them with a smooth curve. Label the coordinates of the intercept in your graph:

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