Leroy shoots a basketball through the air in an attempt to score two points.

The height h of the ball in feet as a function of the distance d in feet that the

ball travels horizontally is given by h = −d^2 + 10d + 5. How far horizontally

from Leroy will the ball land on the ground if it does not hit the backboard or

the rim of the basket?

10.47 feet.

Step-by-step explanation:

The height, h of Leroy's ball is given by the function:

If the ball does not hit the backboard or  the rim of the basket but lands on the ground, then at that point, its height h(d)=0

Therefore:

We solve the above for the values of d.

a=-1, b=10, c=5

Using quadratic formula:

Therefore, the horizontal distance of the ball from Leroy is 10.47 feet.

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!