Question

the polynomial -16t² + vt + h₀ models the height, in feet, of a ball t seconds after it is thrown. in this polynomial, v represents the initial vertical velocity of the ball and h₀ represents the initial height of the ball. min throws a baseball from a height of 6 feet with an initial vertical velocity of 30 feet per second. which polynomial models the height of the ball, in feet? at the same time, mins little brother throws a baseball from a height of 4 feet with an initial vertical velocity of 20 feet per second. what polynomial models the height of this ball, in feet? which polynomial represents the difference in the heights of the baseballs t seconds after they are thrown?

Explanation:

Step1: Identify the polynomials for each ball

Min's ball: The polynomial for height is $- 16t^{2}+30t + 6$ where $v = 30$ (initial - vertical velocity) and $h_0=6$ (initial height). Min's brother's ball: The polynomial for height is $-16t^{2}+20t + 4$ where $v = 20$ and $h_0 = 4$.

Step2: Find the difference of the polynomials

$(-16t^{2}+30t + 6)-(-16t^{2}+20t + 4)$
$=-16t^{2}+30t + 6 + 16t^{2}-20t - 4$
$=(-16t^{2}+16t^{2})+(30t-20t)+(6 - 4)$
$=10t + 2$

Answer:

$10t + 2$