find x and y intercepts of graph of the function

Question

Find x and y intercepts for f(x)=-x^3-3x^2+54x

Answer 1

Shelby,

 

For x intercept y or f(x) is 0 and for y intercept x = 0

 

So when x = 0 in the above equation you get f(x) = 0 hence the y intercept is 0

 

Also when f(x) = 0 we have -x^3 -3x^2 + 54 x = 0

i.e. -x^2 -3x^2 + 54 = 0

or x^2 +3x -54 = 0

x^2 + 9x -6x -54 = 0

x(x+9) -6(x+9) = 0

(x-6)(x+9) = 0

x = 6 and x= -9

Hence the x intercepts are x = 6 and x = -9