Question

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+225

Rewrite this function in the form that reveals when there are no horses occupying stalls at the fairgrounds.

Answer 1

h(x)=-3(x+5)(x-15)

Step-by-step explanation:

Answer 2

Answer:
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The rewritten equation is:

" - 3x² + 30 + 225 = 0 " ;

which is ultimately simplified to:

" x² − 10 − 75 = 0 " .
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The number of days is: "15 days" .
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Step-by-step explanation:
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Given:

h(x) = - 3x² + 30 + 225 ;

Rewrite as: " - 3x² + 30 + 225 = 0 " ;
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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:

"3", "30", and "225" are divisible by "3" ;

{3x² − 30 − 225} / 3 = 0 / 3 ;

to get:
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" x² − 10 − 75 = 0 " ;

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Let us factor:

-15 + 5 = -10 ;

-15 * 5 = -75 ;
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Rewrite as:

(x − 15) (x + 5) = 0 ;

x = 15; and x = -5 ;
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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" .
___________________________________________________