Question

a ball was tossed up into the air. the height of the ball as a function of the time the ball is in the air in seconds can be modeled by a quadratic function. at the time the ball was initially thrown in the air, it was 7.5 meters off the ground. after 1.25 seconds, the ball was at its maximum height of 15.3125 meters. what was the height of the ball 2 seconds after being thrown? round your answer to the nearest tenth as needed. meters

Explanation:

Step1: Escribir la forma vértice de la función cuadrática

La forma vértice de una función cuadrática es $y = a(x - h)^2+k$, donde $(h,k)$ es el vértice. Sabemos que $h = 1.25$ y $k=15.3125$, entonces $y=a(x - 1.25)^2+15.3125$.

Step2: Encontrar el valor de $a$

Cuando $x = 0$, $y = 7.5$. Sustituimos estos valores en la ecuación: $7.5=a(0 - 1.25)^2+15.3125$.
$7.5=a( - 1.25)^2+15.3125$
$7.5 = 1.5625a+15.3125$
$1.5625a=7.5 - 15.3125=-7.8125$
$a=\frac{-7.8125}{1.5625}=-5$.

Step3: Encontrar la altura en $x = 2$

La ecuación de la función es $y=-5(x - 1.25)^2+15.3125$. Sustituimos $x = 2$:
$y=-5(2 - 1.25)^2+15.3125$
$y=-5(0.75)^2+15.3125$
$y=-5\times0.5625+15.3125$
$y=-2.8125+15.3125$
$y = 12.5$.

Answer:

12.5