Word problem

Question

) The height y (in feet) of a ball thrown by a child is given by the formula below where x

 is the horizontal distance in feet from the point at which the ball is thrown. Use this to answer the following questions. 

 

y=−1/16x^2+6x+3

 

 

  a) How high is the ball when it leaves the child's hand?  

 

  b) What is the maximum height of the ball?  

 

  c) How far from the child does the ball strike the ground?  

Answer 1

Step 1:

The height (in feet) of a ball thrown by a child is .

Here is the horizontal distance in feet from the point at which the ball is thrown.

(a)

Find the height from leaves the children hand.

Substitute in to find the intercept.

Hence, the ball was feet above the ground before it was thrown.

(b)

Find the maximum height of the ball.

The vertex form of the general equation is .

Rewrite the equation into vertex form is

Thus, the maximum height of the ball is .

(c)

Find the distance from child the ball strike the ground.

Factor the equation and set both factors equal to zero.

The children far from the ball strike the ground.

Solution:

(a) The ball was feet above the ground before it was thrown.

(b) The maximum height of the ball is .

(c) The children far from the ball strike the ground.