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) = -3^2 + 30x + 225
Rewrite this function in the form that reveals the zeros of the function, which is when there are no horses occupying stalls at the fairgrounds.

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

Step-by-step explanation:

Assuming 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.

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

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

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