Maths-

General

Easy

Question

# The balls are tossed up into the air . The function f(x)= -4.9x^{2} +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 .

Hint:

## The correct answer is: 13 – 12 = 1

### Solution:- We have given two functions of ball A and ball B.

f(x)= -4.9x^{2} +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) = -4.9x^{2} +14.7 x+0.975

In f(x)= -4.9x^{2} +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)= -4.9x^{2} +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 = -4.9h^{2} +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

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