find all y and x intercepts of the graph of the function

Question

Find all y and x intercepts of the graph of the function. F(x)= -x^3-3X^2+54X

Answer 1

Hi Alena,

 

 

OK let find the x intercepts first, these are the point when the graph crosses the x-axis.  Or said another way the points where f(x)= y =0.

 

so we need to solve the following equation for x

 

0 = -x³ -3x² + 54x

 

first we factor out -x

 

0 = -x(x² +3x - 54)

 

now we figure out if we can factor the quadratic  and we can

 

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

 

now we set each factor equal to zero and solve for x

 

-x=0

x = 0                one point is (0,0)   And since x=0 this is also the y intercept

 

x+9=0

x=-9                 another point is (-9,0)

 

x-6=0

x=6                  another point is (6,0)

 

Hope this helps