SOLUTION: What are the coordinates of the apex of: (f*g)(x) if f(x)=x^2+4 and g(x)=x-3

Algebra ->  Functions -> SOLUTION: What are the coordinates of the apex of: (f*g)(x) if f(x)=x^2+4 and g(x)=x-3      Log On


   

Question 154762: What are the coordinates of the apex of:
(f*g)(x) if f(x)=x^2+4 and g(x)=x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean the vertex?


%28f%2Ag%29%28x%29 Start with the given expression


f%28x%29%2Ag%28x%29 Rewrite the function combination


%28x%5E2%2B4%29%2A%28x-3%29 Plug in f%28x%29=x%5E2%2B4 and g%28x%29=x-3



Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28x%5E2%29%2B4%29%28highlight%28x%29-3%29 Multiply the First terms:%28x%5E2%29%2A%28x%29=x%5E3.


%28highlight%28x%5E2%29%2B4%29%28x%2Bhighlight%28-3%29%29 Multiply the Outer terms:%28x%5E2%29%2A%28-3%29=-3%2Ax%5E2.


%28x%5E2%2Bhighlight%284%29%29%28highlight%28x%29-3%29 Multiply the Inner terms:%284%29%2A%28x%29=4%2Ax.


%28x%5E2%2Bhighlight%284%29%29%28x%2Bhighlight%28-3%29%29 Multiply the Last terms:%284%29%2A%28-3%29=-12.


x%5E3-3%2Ax%5E2%2B4%2Ax-12 Now collect every term to make a single expression.


So %28x%5E2%2B4%29%28x-3%29 FOILs to x%5E3-3%2Ax%5E2%2B4%2Ax-12.


This means that %28f%2Ag%29%28x%29=x%5E3-3%2Ax%5E2%2B4%2Ax-12


Since we're looking at a cubic, this means that the polynomial does not have a vertex. Are you sure that you have the right problem?