The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the number of days since the first of June. h(x)=-3x^2+30+225Rewrite this function in the form that reveals when there are no horses occupying stalls at the fairgrounds.
Accepted Solution
A:
Answer: _______________________________________________________ The rewritten equation is:
" - 3x² + 30 + 225 = 0 " ;
which is ultimately simplified to:
" x² − 10 − 75 = 0 " . ___________________________________________________ The number of days is: "15 days" . ___________________________________________________
Rewrite as: " - 3x² + 30 + 225 = 0 " ; __________________________________________________________ Multiply EACH SIDE of the equation by "-1" ; to get rid of the "-3" ;
-1 * {- 3x² + 30 + 225 = 0} ;
to get: " 3x² − 30 − 225 = 0" ;
Divide EACH SIDE of the equation by "3" ; to simplify; since:
x = 15; and x = -5 ; _______________________________________ The number of days cannot be "negative value"; so we stick with:
"x = 15 days" ___________________________________________________ Answer: The rewritten equation is:
" - 3x² + 30 + 225 = 0 " ;
which is ultimately simplified to:
" x² − 10 − 75 = 0 " . ___________________________________________________ The number of days is: "15 days" . ___________________________________________________