Question

Two rockets, A and B, are shot from two different launch pads. The path of rocket A can be represented by the quadratic function A(t) = −(t − 10)2 + 455, where height, A(t), is in meters, and time, t, is in seconds. The path of rocket B is shown below.

Answer 1

Which rocket reaches the highest altitude (in meters) and how much higher does it travel than the other rocket?

Rocket A reaches the highest altitude and it travels 10 meters higher.
Rocket B reaches the highest altitude and it travels 10 meters higher.
Rocket A reaches the highest altitude and it travels 70 meters higher.
Rocket B reaches the highest altitude and it travels 70 meters higher.

Answer 2

@ParthKohli @sammixboo

Answer 3

@rishavraj

Answer 4

@Owlcoffee

Answer 5

@nincompoop

Answer 6

@Catseyeglint911 @imqwerty @whpalmer4

Answer 7

@phi

Answer 8

@♪Chibiterasu can you help?

Answer 9

what is the highest that rocket B reaches, based on the graph ?
any idea ?

Answer 10

I believe that the highest is just about 500? give or take... @phi

Answer 11

@paki

Answer 12

you can read off the number , because they label the peak. what does it say?

Answer 13

uh- 20,525?

Answer 14

is height b the 525?

Answer 15

that is an (x,y) pair
the 20 is the x-axis (or time)
the y value is the height

yes 525

Answer 16

for A
A(t) = −(t − 10)2 + 455

the peak of a parabola (or quadratic as they call it here)
is at its vertex

this equation is in vertex form, so you can read off the vertex
(if you know how... it should be in your notes)

Answer 17

give me a minute ill tell you if i get it or not.

Answer 18

notes - "The vertex form of a quadratic function is given by
f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola." @phi ok? so... im not sure, am i going to be dividin the vertex by something or compare it to height A?

Answer 19

you match up
f (x) = a(x - h)2 + k
with your equation
A(t) = −(t − 10)2 + 455

just focus on the 10 and 455

Answer 20

the idea is 10 matches up with the h and the 455 with the k
the vertex is at (h,k)
so you put in those numbers

and the height is the "y" value of the (h, k) pair. i.e. the 2nd number

Answer 21

Which rocket reaches the highest altitude (in meters) and how much higher does it travel than the other rocket.. what i have so far - {A(t) = −(t − 10)2 + 455}.. What i need 'distance between height' i have the (h) value for height A right? so dont i have to solve something to find height B? [or] is 10 height A and 455 is height B? thats where im confused...

Answer 22

in (h,k) the h is the time and k is the height
so for A, what is its height ?

Answer 23

I thought it was 20 to be honest, yes?

Answer 24

or 10?

Answer 25

still confused... whats confusing is that im using what i see on the graph..

Answer 26

How did you get 20?

you match up
f (x) = a(x - h)2 + k
with your equation
A(t) = −(t − 10)2 + 455

The graph is rocket B. We could figure out its equation (but we don't know it off hand)

the equation A(t) = −(t − 10)2 + 455 is for rocket A
we don't have its graph (but we could plot it)

so we have to use two different ideas to get the height:
for rocket B we look for the vertex and read off the number (easy to do, they tell us the vertex is at (20,525) and the y value (height) is the 2nd number)

for rocket A, we have to use the equation to read off the vertex.
so, what is the (x,y) or in other words (h, k) for rocket A using the *equation*?

Answer 27

OOOOHH see, thats where i got the 20 from.

Answer 28

so far, from the graph we know rocket B reached 525

now we have to use the equation for A to find its height

Answer 29

they already gave us rocket B? makes sense now.

Answer 30

they gave us a graph for B. You still had to figure out that the max height was at 525.

they also give us an equation for A, we still have to figure out its vertex (which you can do if you know how)

Answer 31

well, on a honest note perhaps you can show me how, and then I will try and solve it myself using whatever techniques you've got, eh?

Answer 32

your notes say
***notes - "The vertex form of a quadratic function is given by
f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola."
****

can you match up
f (x) = a(x - h)2 + k
A(t) = −(t − 10)2 + 455

what does "h" match up with
what does "k" match up with ?

Answer 33

uh h -10? and k 455?

Answer 34

almost. notice that the (x-h) matches with (t-10)
the x /t match up
the - /- match up
the h / 10 match
in other words h matches with 10 (not -10)
that means the vertex (h, k) is at (10,455)

Answer 35

ok

Answer 36

now that you know the vertex for rocket A, you know its max height

Answer 37

max is 455?

Answer 38

if so do i subtract A and B's max hieghts?

Answer 39

yes, remember in (10, 455) the first number is how far sideways we go, and the 2nd number is how far up or down. we want the up/down number

Answer 40

heights*

Answer 41

The very first thing I do is write down what we know
A 455
B 525
which is higher ? B!
then I would look at the choices and cross off any that say A is higher

Answer 42

so rocket b reaches highest at altitude 70, yes?

Answer 43

you mean B goes 70 meters higher than A
in other words if we go to 455 meters then go another 70 meters
455+70= 525 meters , we get to B's height.

Answer 44

sorry couldnt paste so i wrote it in my own words... meant to say "Rocket B reaches the highest altitude and it travels 70 meters higher."

Answer 45

yes, that is good.

Answer 46

thanks you :D