# Math Help - Can anyone please help me with this maths investigation problem? ):

1. ## Can anyone please help me with this maths investigation problem? ):

At the start of the chapter you were given an equation which modelled the leap of
a dolphin as it ‘flew’ out of the water. The equation is h = −0.4d2 + d, where h is
the dolphin’s height above water and d is the horizontal distance from its starting
point. Both h and d are in metres.
1 How high above the water is the dolphin when it has travelled 2 m horizontally
from its starting point?
2 What horizontal distance does the dolphin cover when it first reaches a height of
25 cm?
3 What horizontal distance does the dolphin cover when it next
reaches a height of 25 cm? Explain your answer.
4 What horizontal distance does the dolphin cover in one leap?
(Hint: What is the value of h when the dolphin has completed
its leap?)
5 Can this dolphin reach a height of:
a 0.5 m? b 1 m during a leap?
How can you work this out without actually solving the
equation?
6 Find the greatest height that the dolphin reaches during a leap.

*I REALLY NEED YOUR HELP. ): I DON'T WANNA GET AN E.

2. ## Re: Can anyone please help me with this maths investigation problem?

The equation is $h=-0.4d^2+d.$

1. Substitute $d=2$ into the equation and work out what $h$ is.

2 & 3. Let $h=0.25.$ Thus $0.25=-0.4d^2+d;$ moving all the terms to the left, $0.4d^2-d+0.25=0.$ Solve this quadratic equation for $d.$ You will get two values; the smaller value is the answer to 2 and the bigger value that to 3.

4. Hint: $h=0.$

5 and 6. Hint: $h = -0.4d^2+d = -0.4(d^2-2.5d) = -0.4\left[(d-1.25)^2-1.5625\right].$

3. ## Re: Can anyone please help me with this maths investigation problem? ):

Thankyou so much! :d

4. ## Re: Can anyone please help me with this maths investigation problem? ):

Hey guys! I need a thorough explanation of every answer. Although the answer was given there above my teacher wanted the answers to have explanations. No matter how I try it seems I can't explain a thing. ): Yeah as you can see I suck at Maths. That's why I really need your help. I'm trying my best to have an A+ as a grade so PLEASE. It would really make me happy if someone will do it.

5. ## Re: Can anyone please help me with this maths investigation problem? ):

NOTE: There were added questions.
What horizontal distance does the dolphin cover if it performs 3 leaps in a row?
Think how can you work this out without actually solving quadratic equations?
Find the greatest height that the dolphin reaches during a leap. Apply 3 different approaches to solve "the maximum height" problem.
Here are the 3 different approaches: Completing the square, line of symmetry of the parabola and I actually don't know the last one. Haha! Can you think what other approaches could I use? HELP. ):

-- I HOPE YOU COULD HELP ME. THANKYOU!

6. ## Re: Can anyone please help me with this maths investigation problem? ):

*How is question 5? Help please. ): I need to pass our assignment tomorrow. I am so desperately needing help right know. :/

7. ## Re: Can anyone please help me with this maths investigation problem?

Originally Posted by jaizzerzerzer
NOTE: There were added questions.
What horizontal distance does the dolphin cover if it performs 3 leaps in a row?
Think how can you work this out without actually solving quadratic equations?
In Q4 you worked out the distance the dolphin travelled in one leap. So if it leaps three times, how far does it travel?

Originally Posted by jaizzerzerzer
Find the greatest height that the dolphin reaches during a leap. Apply 3 different approaches to solve "the maximum height" problem.
Here are the 3 different approaches: Completing the square, line of symmetry of the parabola and I actually don't know the last one. Haha! Can you think what other approaches could I use? HELP. ):
The last approach is calculus.

8. ## Re: Can anyone please help me with this maths investigation problem? ):

Oh. I get it now! Thanks! (: I get it a little. Haha. But thankyou so much! I just got one more question, how will you do the completing the square? Are you gonna use the 0.25 and combine it with the equation? Could you please show how? PLEEEEAAAASSSEE. I'm kinda still confused about it.

9. ## Re: Can anyone please help me with this maths investigation problem?

I already completed the square for you above.

10. ## Re: Can anyone please help me with this maths investigation problem?

Oh. The one with number 5 and 6? I'm so sorry if I'm frustrating you. Sorry. So the above equation you did was already completed? How will you do this if y=(x-h)^2+k then you will get the turning point h=x-intercept and k=y-intercept of the turning point. How is that? The equation above wasn't the same as the y=(x-h)^2+k.