Question

Describe the graph of the function f(x) = x3 − 15x2 + 68x − 96. Include the y-intercept, x-intercepts, and the end behavior.

Answer 1

in the form
f(x)=
`ax^(n)+bx^(n-1)...+z`
a=leading term,
z=contstant aka y intercept

this is 3rd degree (highest term is x^3) with leading term positive so the graph goes from bottom left to top right
x intercept is when y=0 so
0=x^3-15x^2+68x-96
factor
(x-8)(x-4)(x-3)
these are your roots aka zeroes (where the line crosses the x axis)
the roots are
(x-r) where r=root aka x intercept

so we have
(x-8)(x-4)(x-3)
roots are
8,4,3
x intercepts are 8,4,3 or (8,0),(4,0),(3,0)

y intercept is when x=0 so just get rid of all x terms and we are left with
-96
aka y intercept=(0,-96)






x intercepts=(8,0),(4,0),(3,0)
y intercept=(0,-96)
end bhavior is graph goes from bottom left to top right