SOLUTION: a) Sketch the polynomial defined by the following: f(x) is cubic f(x) ≥ 0 when x ≤ 2 f(x) < 0 when x > 2 f(0) = 4 b) Write an equation for f(x) in general form. I ne

Algebra ->  Inequalities -> SOLUTION: a) Sketch the polynomial defined by the following: f(x) is cubic f(x) ≥ 0 when x ≤ 2 f(x) < 0 when x > 2 f(0) = 4 b) Write an equation for f(x) in general form. I ne      Log On


   



Question 1182973: a) Sketch the polynomial defined by the
following:
f(x) is cubic
f(x) ≥ 0 when x ≤ 2
f(x) < 0 when x > 2
f(0) = 4
b) Write an equation for f(x) in general form.
I need your help!! thanks

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In order for it to be positive before and negative after x=2, then it must look like this,
f%28x%29=a%28x-2%29%5E3
or else you will have an additional set of directional changes.
So now solve for the constant.
After x=2+the cubic will be positive so the constant needs to be negative.
So,
f%28x%29=-a%28x-2%29%5E3
f%280%29=-a%280-2%29%5E3=4
a=4%2F8
a=1%2F2


f%28x%29=-%281%2F2%29%28x-2%29%5E3

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%281%2F2%29%28x-2%29%5E3%29+