**Case Study -1**

The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.

Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t^{2} + 8t + k.

Rita’s height (in feet) above the water level is given by another polynomial p(t) with zeroes -1 and 2. Then p(t) is given by ______.

#### Options

t

^{2}+ t - 2t

^{2}+ 2t - 124t

^{2}- 24t + 48-24t

^{2}+ 24t + 48

#### Solution

Rita’s height (in feet) above the water level is given by another polynomial p(t) with zeroes -1 and 2. Then p(t) is given by **-24t ^{2} + 24t + 48**.

**Explanation:-**

t = -1 and t = 2 are the two zeroes of the polynomial p(t)

Then p(t) = k (t - (-1))(t - 2)

= k(t + 1)(t - 2)

When t = 0 (initially) h_{1} = 48ft

p(0) = k(0^{2 }- 0 - 2) = 48

i.e. -2k = 48

So the polynomial is -24(t^{2} - t - 2) = -24t^{2} + 24t + 48.