The balls are tossed up into the air . The function f(x)= -4.9x² +14.7 x+0.975 models the path of Ball A. the path of ball B over time is shown in the table. Which ball reaches a greater height ? How much greater . Explain how you can answer without graphing either function .

The correct answer is: 13 – 12 = 1

Solution:- We have given two functions of ball A and ball B.
f(x)= -4.9x² +14.7 x+0.975

We have to find the ball which reaches the greater height.
For that we will find the vertex of both the functions
For f(x) = -4.9x² +14.7 x+0.975
In f(x)= -4.9x² +14.7 x+0.975,  a= -4.9, b= 14.7, and c= 0.975. So, the equation for the axis of symmetry is given by
x = −(14.7)/2(-4.9)
x = -14.7/-9.8
x = 1.5
The equation of the axis of symmetry for f(x)= -4.9x² +14.7 x+0.975 is x = 1.5.
The x coordinate of the vertex is the same:
h = 1.5
The y coordinate of the vertex is :
k = f(h)
k = -4.9h² +14.7h +0.975
k = -4.9(1.5)² +14.7(1.5) + 0.975
k = -11.025+22.05+0.975
k = 12
Therefore, the vertex of curve of ball A is (1.5 , 12)
So , the maximum height of ball A is 12
For ball B after observing the given table we have the maximum value of g(x) as 13, which is the maximum height of the ball.
So, the ball B reaches at the greater height of 13.
Difference between heights of ball A and ball B is 13 – 12 = 1