Question

The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the number ofdays since the first of June.A(s) = -322 + 301 + 225Rewrite this function in the form that reveals the zeros of the function, which is when there are no horses occupying stalls at the fairgrounds.(0) JOUsin cos tan sin cos'tan9o2 AnΣXva0>2csc seccot log log inh(x) =

Answer 1

The number of horses occupying the country fairground is modeled by

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

To rewrite the function in the form that reveals the zeroes of the function

Zeroes of the function h(x) are those values of x for which the equation h(x)=0 is satisfied.

On factorizing, we have

$\begin{gathered} h(x)=-3(x^2-10x-75) \\ =-3(x^2-15x+5x-75) \\ =-3\lbrack x(x-15)+5(x-15)\rbrack \\ =-3(x-15)(x+5) \end{gathered}$

Hence, h(x) can be expressed in the form that reveals the zeroes as

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

Now, from the equation h(x)=0, the zeroes can be evaluated by

$\begin{gathered} -3(x+5)(x-15)=0 \\ x=-5 \\ x=15 \end{gathered}$