Solution-
The profit function given in the question,
[tex]P(x)=5.152x^3-143x^2+1102x-1673[/tex]
Where,
x = the number of houses built in a year
We can calculate y-intercept by putting x=0, so
[tex]=5.152(0)^3-143(0)^2+1102(0)-1673[/tex]
[tex]=0-0+0-1673[/tex]
[tex]=-1673[/tex]
y-intercept is -1673, i.e when x=0 or the number of houses built is 0, their profit is -1673. Actually it is not the profit, but loss. So if they don't build any house, they will lose $1673
We can calculate x-intercept or zeros by putting y=0, so
[tex]5.152x^3-143x^2+1102x-1673=0[/tex]
Calculating the zeros by graphing calculator, they are as follows,
[tex]x=2,\ 11.019,\ 14.737[/tex]
x-intercept shows that they need to built at least 15 (as number house can not be fraction) houses, in order to start profiting. Even though they start profiting after building 2 houses, but then the profit starts decreasing and reaches 0 again and so does happen after building 11th house. (It might happen due to the other costs and investments used for building the houses ). But after finally building 15th house they start profiting.
