The height y (in feet) of a ball thrown by a child is y = − 1/14x^2 + 6 x + 3 where x is the horizontal distance in feet from the point at which the ball is thrown. how high is the ball when it leaves the child's hand? (hint: find y when x = 0)your answer is y= (b) what is the maximum height of the ball? (c) how far from the child does the ball strike the ground?

Step-by-step explanation:

The given equation,

where,

x is the horizontal distance in feet and

y is the height of the ball in feet.

How high is the ball when it leaves the child's hand.

At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.

What is the maximum height of the ball.

As the quadratic function has negative leading coefficient, so it will open downwards and at the vertex we will get the maximum value of the function.

The coordinates of vertex are,

Putting the values,

Now,

How far from the child does the ball strike the ground.

At the end i.e when the ball touches the ground, the height of the ball is 0. So putting the value of y=0, in the equation,

Solving the quadratic equation, we get

As distance can not be negative, so only considering positive value,

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet