A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
f(x) = 16t^2 + 96t
what is the x and y intercept
anonymous
 one year ago
f(x) = 16t^2 + 96t what is the x and y intercept

This Question is Closed

freckles
 one year ago
Best ResponseYou've already chosen the best response.1where is the function of x? is t suppose to be x?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well I mean that could be a function of x it would just be a constant function of x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://assets.openstudy.com/updates/attachments/53ce7ea6e4b081ba963957d9coltjoco1406041829668paulkicks.jpg this is the graph

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436976311744:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436976350942:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1the xintercepts are the points where the function is equal to 0 the yintercept is the point where x = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is the x intercept 1,6?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1yes, or more specifically (1,0) and (6,0)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also could you help me with a few more questions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find the vertex algebraically. Write as an ordered pair.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the maximum height of the ball? Write your answer as an integer.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1(1,0) isn't on the graph though :p

freckles
 one year ago
Best ResponseYou've already chosen the best response.1(0,0) and (6,0) if we are talking about the function in the graph

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x) = 16t^2 + 96t \] so I guess that that one x was suppose to be a t :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find the vertex algebraically. Write as an ordered pair. would the vertex 6,0 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1wait and it looks like they called the function h(t) instead of f(t)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the vertex would be that peak point

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if you wanted to find it using that graph you could observe that the vertex occurs midway between the xintercepts

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I will also show you how to find it algebraically since you asked

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but first using the graph the vertex appears to be at (3,a little above 140) I will let you approximate that y value

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but anyways algebraically ...

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y=at^2+bt+c \\ \text{ we want to put this in vertex form } \\\] \[yc =at^2+bt \text{ I subtract } c \text{ on both sides } \\ \frac{yc}{a} =t^2+\frac{b}{a} t \text{ I divided both sides by } a \\ \frac{yc}{a} +(\frac{b}{2a})^2=t^2+\frac{b}{a}t +(\frac{b}{2a})^2 \\ \text{ I threw in a number on both sides so I could } \\ \text{ complete the square on one side } \\ \frac{yc}{a}+(\frac{b}{2a})^2= (t+\frac{b}{2a})^2 \\ \text{ now \let's reisolate } y \\ \text{ subtract} (\frac{b}{2a})^2 \text{ on both sides } \\ \frac{yc}{a}=(t+\frac{b}{2a})^2(\frac{b}{2a})^2 \\ \text{ multiply } a \text{ on both sides } \\ yc=a(t+\frac{b}{2a})^2a (\frac{b}{2a})^2 \\ \text{ add } c \text{ on both sides } \\ y=a(t+\frac{b}{2a})^2a(\frac{b}{2a})^2+c\] the vertex is given by: \[(\frac{b}{2a},a(\frac{b}{2a})^2+c)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03o would the vertex be 3,14 or 3,140?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1look at the graph you should see where that mountain's peak is just a hair above 140 the y value isn't exactly 140 it is just above 140

freckles
 one year ago
Best ResponseYou've already chosen the best response.1it is closer to 140 than 160

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436977378401:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436977410220:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1how is 120 just a little above 140 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can find the ycoordinate of the vertex exactly by using the steps I gave you above

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry I was confused

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but you can approximate it using the visual it looks like it could be maybe less than 150 but greater than 140 and I say less than 150 because the peak doesn't reach halfway between 140 and 160 it is less than halfway I would approximate saying 142 but that could be off a little because I did find this visually and not algebraically as the instructionsdw:1436977561263:dw suggested

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436977596987:dw so you know the vertex is gonna be somewhere close to (3,142)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can find the answer algebraically using the method above I suggested

freckles
 one year ago
Best ResponseYou've already chosen the best response.1this one: \[yc =at^2+bt \text{ I subtract } c \text{ on both sides } \\ \frac{yc}{a} =t^2+\frac{b}{a} t \text{ I divided both sides by } a \\ \frac{yc}{a} +(\frac{b}{2a})^2=t^2+\frac{b}{a}t +(\frac{b}{2a})^2 \\ \text{ I threw in a number on both sides so I could } \\ \text{ complete the square on one side } \\ \frac{yc}{a}+(\frac{b}{2a})^2= (t+\frac{b}{2a})^2 \\ \text{ now \let's reisolate } y \\ \text{ subtract} (\frac{b}{2a})^2 \text{ on both sides } \\ \frac{yc}{a}=(t+\frac{b}{2a})^2(\frac{b}{2a})^2 \\ \text{ multiply } a \text{ on both sides } \\ yc=a(t+\frac{b}{2a})^2a (\frac{b}{2a})^2 \\ \text{ add } c \text{ on both sides } \\ y=a(t+\frac{b}{2a})^2a(\frac{b}{2a})^2+c\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0though I think it may be 3 I'm not sure

freckles
 one year ago
Best ResponseYou've already chosen the best response.1are you trying to put your quadratic in vertex from yet?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm still using the graph for it

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oh okay well don't forget it does say to find the vertex algebraically

freckles
 one year ago
Best ResponseYou've already chosen the best response.1using a graph to obtain the vertex is not finding it algebraically

freckles
 one year ago
Best ResponseYou've already chosen the best response.1are you talking about the xcoordinate of the vertex?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1no 3 is not the xcoordinate

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436978591061:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the vertex is pretty close to (3,142) or I guess you could say (3,141) but we don't know the vertex exactly until you find it algebraically

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but to find out we need to put your quadratic in vertex form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I gave a general way to do that above

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436979098053:dw please look at this graph... dw:1436979115849:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1again this is not finding the vertex algebraically this is approximating the vertex with the help of visual aid you can find the exact vertex by putting the quadratic into vertex form you will need to complete the square

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y=16t^2+96t \\ \text{ factor out 16 } \\ y=16(t^26t) \\ y=16(t^26t+?)+16(?)\] what do you need to add inside the ( ) to complete the square

freckles
 one year ago
Best ResponseYou've already chosen the best response.1no recall that: \[x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the number in front of t is 6 let's call k, 6 so if k=6 then k/2=?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y=16t^2+96t \\ \text{ factor out 16 } \\ y=16(t^26t) \\ y=16(t^26t+(\frac{6}{2})^2)+16(\frac{6}{2})^2\] right can you finish putting into vertex form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1by the way I didn't put the  in because (6/2)^2 is the same as (6/2)^2 but you could have

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we already know we are suppose to get something close to (3,142) because this what we found visually

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so I don't know what 6 is suppose to be

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but anyways I was asking if you could finish putting into the vertex form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1i have to ask are you playing with me?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1like you keep giving me these y values that aren't closer to 140

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no I'm not i'm really stuck on this equation

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I have shown you visually the yvalue is a little above 140 we know the xvalue to be exactly 3 the vertex is definitely somewhere close to (3, 142)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which I had gotten 141

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y=16t^2+96t \\ \text{ factor out 16 } \\ y=16(t^26t) \\ y=16(t^26t+(\frac{6}{2})^2)+16(\frac{6}{2})^2 \\ y=16(t3)^2+16(\frac{6}{2})^2 \] there I completed the square for you

freckles
 one year ago
Best ResponseYou've already chosen the best response.1as we see the xcoordinate of the vertex is 3 just evaluate 16(6/2)^2 to find the y coordinate of the vertex

freckles
 one year ago
Best ResponseYou've already chosen the best response.1@Aliypop yes I see you said 141 as approximate but then you asked me if it was 2,14,... and so on...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I confused on what the x value is

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the xcoordinate of the vertex is 3 we have found this both visually and algebraically now

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the ycoordinate of the vertex is given by 16(6/2)^2 which we have approximated to be somewhere just above 140

freckles
 one year ago
Best ResponseYou've already chosen the best response.1again 3 is nowhere near 140

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the xcoordinate of the vertex is 3 the ycoordinate of the vertex is something just above 140 we have found this information visually we have also found algebraically the xcoordinate of the vertex is 3 the ycoordinate of the vertex is 16(6/2)^2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y=16t^2+96t \\ \text{ factor out 16 } \\ y=16(t^26t) \\ y=16(t^26t+(\frac{6}{2})^2)+16(\frac{6}{2})^2 \\ y=16(t3)^2+16(\frac{6}{2})^2 \\ \text{ this says the vertex is } (3,16(\frac{6}{2})^2)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1all you have to do is finishing simplifying

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you need help doing 16(6/2)^2?

freckles
 one year ago
Best ResponseYou've already chosen the best response.16 divided by 2 is 3 3 squared is 9 16*9 is...

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes \[y=16t^2+96t \\ \text{ factor out 16 } \\ y=16(t^26t) \\ y=16(t^26t+(\frac{6}{2})^2)+16(\frac{6}{2})^2 \\ y=16(t3)^2+16(\frac{6}{2})^2 \\ \text{ this says the vertex is } (3,16(\frac{6}{2})^2) =(3,144)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the vertex is exactly (3,144)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1as we see this makes sense from our visual answer because we did say the vertex had xcoordinate 3 and ycoordinate of something just above 140

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the maximum height of the ball? Write your answer as an integer. this was the other question i need help on

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you actually already found this when you found the vertex the vertex is the highest point and you know the yvalue represents the height

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436980560407:dw yes the height is 144 and the time in which the height is 144 is t=3 sec if the time unit is second

freckles
 one year ago
Best ResponseYou've already chosen the best response.1though usually you would say 144 units where units is some kind of distance measurement but that isn't really given here
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.