Question

I really need help I would appreciate it if someone could help me

Answer 1

Answer:

a) The vertex of the graph is $(h,k) = (0, 31)$, b) $a = -16$, c) The equation of the parabola is $f(t) = -16\cdot t^{2}+31$.

Step-by-step explanation:

a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.

The vertex of the graph is $(h,k) = (0, 31)$.

b) If we know that $(h,k) = (0, 31)$, $f(t) = a\cdot (t-h)^{2} + k$ and $(t,f(t)) = (1,15)$, then the value of $a$ is:

$f(t) = a\cdot (t-h)^{2} + k$

$15 = a\cdot (1-0)^{2}+31$

$15 = a\cdot 1 + 31$

$a = 15-31$

$a = -16$

c) The equation of the parabola is $f(t) = -16\cdot t^{2}+31$.