Question

Adam kicks the football in his backyard. The path of the football when kicked can be represented by the quadratic function y = - 16x^2 + 85x where x is the horizontal distance (in feet) and y is the height (in feet). How far does Adam kick the football? Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

well to find the horizontal distance travelled by the ball, let y = 0.., so the ball is on the ground,

so

\[0 = x(-16x + 85)\]

so I'll do the easy solution x = 0 you can find the other by solving

-16x + 85 = 0

Answer 2

if you need the vertical height, because the path of the ball is a parabola, just find the line of symmetry

x = -b/2a so x = -85/32

substitute the x value to find the max height.

Answer 3

oops should be x = -85/-32

Answer 4

2.65625 ?

Answer 5

well start with the horizontal distance

x = 5.3125..... so the ball travels 5.3125 ft

Answer 6

its interesting in that the ball gets to a highest point of 112.89 feet

Answer 7

is that rounded ?

Answer 8

well hundredths is 2 decimal places...

so round 5.3125 to 2 decimal places

Answer 9

so is it 5.31

Answer 10

yep... thats the horizontal distance travelled.

Answer 11

Its wrong

Answer 12

it said this when i got it wrong ? Use your graphing calculator to find the solution.

Answer 13

so what distance are you being asked for... the horizontal distance or the vertical height.

Answer 14

do you have a graphing calculator..?

Answer 15

Horizontal Im guessing. It says nothing about vertical. and yes i do .

Answer 16

here is a copy of the graph of your curve. hope this helps

Answer 17

so I'd press the y = key and type in the equation... and then find the zeros.

Answer 18

I typed it in y= what do after ?

Answer 19

press enter and you should get the curve on your screen

Answer 20

i dont i get a line going down

Answer 21

you may need to press the window key, and resize y max = 120 y scl 10

and x max = 6

Answer 22

ok i did

Answer 23

what do i do after

Answer 24

next you have a trace key...?
and above it in yellow you have CALC

Answer 25

correct

Answer 26

press the 2nd key and then CALC

you get a list of options...

select zero

Answer 27

ok done

Answer 28

then using the arrow keys move the curser to a point just below the point where the curve cuts the x axis, press enter and then move the curser again to a point above the cut.. press enter... and I think you have to press enter again. It will then give a value for the zero

Answer 29

I haven't done this in ages... so it may not work

Answer 30

the numbers just keep going up for x and y

Answer 31

ok...

so just press 2nd and CALC again

Answer 32

kk

Answer 33

and you get a menu list

press the number on the keypad that matches zeros

Answer 34

wait what ? so 2

Answer 35

yep

you should be back with the graph and somewhere on the screen it says lower bound

Answer 36

It says left not lower ..

Answer 37

ok... thats fine, type in 3

when you get right type in 8...

these values should eb either side of the point where the curve cuts the x axis

I think its 3 enter, then 8 enter

Answer 38

after that is it says estimate just press enter

Answer 39

you should get a number displayed on the screen for of around 5.3

its the max horizontal distance

Answer 40

once i enter 3 its y=511 but once i try 8 it says Error invalid

Answer 41

its not letting me type 8

Answer 42

try 6

Answer 43

it says y= 766

Answer 44

ok... well I'm only guessing now at how to use your calculator..

just try putting in the vertical height 112.89.

the maths in finding the horizontal distance is correct... 5.3125 ft

so I don't know where to go

Answer 45

ok so you dont know for sure the final answer ?

Answer 46

No, the mathematics is correct. Its just which answer do you need. If you graph the equation it cuts the x-axis at 0, 5.3125