Question

Find x and y intercept and sketch graph
1.f(x)= -(x+3)^2(x+1)(x-2)^2(x-4)
2.g(x)=(x+3)^2(x+1)(x-2)(x-4)^2

Answer 1

x-intercepts are also known as the roots or zeroes, i.e. where the function intersects y = 0; equate each function to 0 and solve for x.
y-intercepts are just the value of the functions for x = 0; plug in 0 to both to determine these.

1.
i.
f(x)=0
-(x+3)^2(x+1)(x-2)^2(x-4)=0
x=-3,-1,2,4
(-3,0), (-1,0), (2,0), (4,0) are all x-intercepts of f

ii.
f(0)=-(3)^2(1)(-2)^2(-4)=-9*4*-4=144
(0,144) is the y-intercept of f

2.
i.
g(x)=0
(x+3)^2(x+1)(x-2)(x-4)^2=0
x=-3,-1,2,4
(-3,0), (-1,0), (2,0), (4,0) are all x-intercepts of f

ii.
g(0)=(3)^2(1)(-2)(-4)^2=-288
(0,-288) is the y-intercept of f

Answer 2

thank you :D
One more question, can you show me how to solve :

\[f(x)\ge0\]
With the same info given above

Answer 3

f(x)>=0 means either f(x)=0 or it's positive; knowing a positive times a negative is a negative while a positive times a positive or a negative times a negative results in a positive, you need to map out the different possible ways each function could be positive by identifying the possible signs of each factor. it's too much work for me to do right here but trust me when i say it's easy but tedious. http://www.purplemath.com/modules/ineqpoly.htm

Answer 4

thanks for all your help :)