Question

DESPERATE FOR HELP!!! Please help - I will award medals.
An archer releases an arrow from a shoulder height of 1.39m. When the arrow hits the target 18m away, it hits point A. When the target is removed, the arrow lands 45m away. The distance from the top edge of the archery target to the ground is 1.5m. Find the maximum height of the arrow along its parabolic path. Point A is 24cm down from top of target. *** I can't figure out which is a, b, and c.

Answer 1

it's a derivative problem.find local extrema

Answer 2

I don't know what the points are to put in to solve

Answer 3

u don't need points, find the function, then take the derivative of it

Answer 4

y = f(x) = ax² + bx + c
and the max height will be x = -b/(2a)
I'm stuck after that

Answer 5

a, b, and c are given, u should only have x as a variable

Answer 6

yes but I cannot figure out a,b,c to use quad equation

Answer 7

I tried it as linear regression but that didn't work out either

Answer 8

try drawing a triangle and labeling the sides

Answer 9

don't I need points like (2,10), (4,12) for example to come up with a,b,c?

Answer 10

lol...

Answer 11

I'm sorry - don't mean to be stupid but I am just not getting this at all

Answer 12

those values in the problem are given for a reason

Answer 13

yea it's ok

Answer 14

i didnt mean lol in the mocking way...

Answer 15

would it be (18,1.39) , (45,1.5), (0,0)?

Answer 16

yes u can try that

Answer 17

I did but it doesn't work. What is a,b,c? Then I can plug into equation.

Answer 18

Yes it is -b/2a that you have to find.

But the original equation is y = f(x) = ax² + bx + c

You are given 3 points on the curve and you have 3 unknowns a, b and c and so you can solve for them.

x = 0, y = 1.39
x = 45, y = 0
x = 18, y = (1.5 - .24)

Substitute and solve for a and b. Eliminate c as you don't need it to find -b/2a

Answer 19

why did you put y=(1.5-.24) on the last equation?

Answer 20

ok - when I put those in I get a=-0.0008765 b=0.0085556 c=1.39
when I solve y=-0.00087654321x^2+0.008555556+1.39
even if I solve for x that isn't giving me the height. What am I doing wrong?

Answer 21

duh - I didn't do the second step for -b/2a. ok. when I do that I get -4.88

Answer 22

Assuming your a, b and c are correct you just plug in to the equation you had for maximum height -b/2a

Answer 23

can a height be a negative?

Answer 24

It depends on how the parabola is oriented.
But for this problem I would expect a positive height.
-b/2a. Your b is positive and a is negative so -b/2a should be positive.

Answer 25

I put in -0.0085556/2(-0.0008765) => -0.008556/-0.001753=-4.88

Answer 26

a negative divided by a negative is positive.

Answer 27

I have spent over 2 hours on this question and am brain dead. The calculator also gave me a negative number

Answer 28

Do you know if the answer is 4.88 meters?

Answer 29

not for sure. That's what I came up with.

Answer 30

Is this problem from a textbook or online? Will you only know if it is right or wrong after submitting the answer and wait for the teacher to tell you?

Answer 31

It's a homework question. No, I won't be submitting it online. I have to write it out and turn in

Answer 32

The 4.88 is correct if your a, b and c are correct. One way to check if its is correct is to put back the x values of the three points on the curve and see if it matches the y values. I already know your c is correct because when x = 0, y = c = 1.39

Answer 33

Can I ask for help for 1 other question? I did it as a linear regression but I know it isn't right. Well - my answer for linear regression is right but I don't think that's how I'm supposed to answer it. The question is: The table shows how the weight and height of an arrow affects it. Graph the data in the table to find a linear and a quadratic model for the data. Which model is a better fit. The chart is:
140 150 170 175 205 on top and underneath is 1.4 1.25 0.93 0.78 0.43

Answer 34

Did you use a standard formula for linear regression and if so do you have a formula for quadratic model?

Answer 35

no. I put it into the calculator without understanding what I was doing and the calculator gave me the linear regression

Answer 36

It gave me : mean x=168 mean y=0.958 intercept(a)3.51 slope(b) -0.12 and y=3.51-0.015x

Answer 37

If you are allowed to use calculators then there are good linear regression calculators and quadratic regression calculators online where you just put in the x,y values from the table and the calculator will give you the regression equation.
Here is one quadratic regression calculator: http://www.had2know.com/academics/quadratic-regression-calculator.html

Answer 38

y = -0.0018x^2 - 0.2696x + 123.108 is what that gave me from that calculator

Answer 39

Here is a linear regression calculator: http://ncalculators.com/statistics/linear-regression-calculator.htm

Answer 40

Regression Equation Y=3.5125 + -0.0152 x

Answer 41

do I graph both to see which is a straighter line?

Answer 42

So the equations for the linear and quadratic regressions will be the answer to the question: find a linear and a quadratic model for the data.

To find out which is a better fit, I think you will need to find something called a correlation coefficient r. Whichever one gives an r closer to 1 is the better model. My statistics is a bit rusty though. Haven't used it in a long time.

Answer 43

If you graph those two regression lines, the linear one will be a straight line and the quadratic one will be a curve (a parabola).

Answer 44

I haven't taken statistics yet - only the portion we did in geometry last year and I don't remember a correlation coefficient. I will have to go back to my notes.
Thank you so much for your time and knowledge. I was ready to through my book I was getting so upset at not understanding what I was doing. I'm glad they let us use calculators but sometimes I think I don't learn it as well because I'm not always sure where I'm pulling the numbers from to plug in.

Answer 45

You are welcome. In the first problem, put back those three data points to make sure the a, b, c that you solved are correct. If they are then 4.88 meters is the correct answer.

Answer 46

Thank you. I will do that now.