Question

WORTH 98 POINTS

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

The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.

Explanation:

I assume an x is missing, and the function is h(x) = -3x^2 + 30x + 225

You want to know the number of days in which the function value is zero.

-3x^2 + 30x + 225 = 0

Divide both sides by -3.

x^2 - 10x - 75 = 0

(x - 15)(x + 5) = 0

x - 15 = 0 or x + 5 = 0

x = 15 or x = -5

We discard the negative solution.

Answer: The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.

Answer 2

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

Explanation:

h(x) = -3x^2 + 30 + 225

= -3(x^2 - 10x - 75)

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

x = -5 x = 15