Question

Find all x-intercepts and y-intercepts of the graph of the function.
F(x)=x³-4x² - 4x + 16

Answer 1

Answer: (0;16) (4;0) (2;0) (-2;0).

Explanation:

Y-intercepts of the graph of the function F(x)=x³-4x² - 4x + 16:

`x=0\\F(x)=0^3-4*0^2-4*0+16\\F(x)=16.\\Hence,\ (0;16).`

X-intercepts of the graph of the function F(x)=x³-4x² - 4x + 16:

`F(x)=0\\0=x^3-4x^2-4x+16\\0=(x^3-4x^2)-(4x+16)\\0=x^2*(x-4)-4*(x-4)\\0=(x-4)*(x^2-4)\\0=(x-4)*(x^2-2^2)\\0=(x-4)*(x-2)*(x+2)\\x-4=0\\x_1=4.\\Hence,\ (4;0)\\x-2=0\\x_2=2.\\Hence,\ (2;0)\\x+2=0\\x_3=-2.\\Hence,\ (-2;0).`