The height y (in feet) of a ball thrown by a child is where x is the horizontal distance in feet from the point at which the ball is thrown a).how high is the ball when it leaves the child's handb).what is the maximum high of the ballc).how far from the child does the ball strike the ground

a) 3 ft

b) 67 ft

c) 64.741 ft.

Step-by-step explanation:

Let as consider the height y (in feet) of a ball thrown by a child is

where x is the horizontal distance in feet from the point at which the ball is thrown

.

(a)

We need to find the initial height of the ball.

Substitute x=0 in the given equation.

Therefore, the height of ball is 3 ft when it leaves the child's hand.

(b)

If a quadratic equation is defined as

then the vertex of the function is

In the given equation and b=4. So,

Substitute x=32 in the given equation.

The vertex of the parabola is (32,67). So, the maximum height of the ball is 67 ft.

(c)

The height of the ball is zero when it touch the ground.

Substitute y=0 in the given function.

Using quadratic formula, we get

The distance can not be negative. So the ball will touch the ground at the distance of 64.741 ft.

312312

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!