1. ## Yr 10 Maths Level 1:Quadratics Investigation

the equation is h=-0.4 d^2 + 2d.

h=height above water, d=horizontal distance.

Q1) how high above the water is the dolphin when it has travelled 2 m horizontally from its starting point?

A1) h=-0.4 (2)^2 + (2)
h=-1.6 + 2
h=0.4m
(im fairly sure that this is correct)

Q2) what horizontal distance does the dolphin cover when it first reaches a height of 25cm?

A2) 0.25=-0.4 d^2 + 2
0.25 + 0.4 = d^2 + d
0.65=d^2 +2
square root of 0.65=d + d
0.81= d+d
0.81/2=d
0.405m =d

Q3) what horizontal distance does the dolphin cover when it next reaches a height of 25cm? explain.

A3) i am unsure of this answer

Q4)what horizontal distance does the dolphin cover in one leap? (hint:what is the value of h when the dolphin has completed the leap?)

A4) i am unsure of this answer

Q5) can this dolphin reach a height of:
a)0.5 m
b)1 during a leap?
How can you work this out without actually solving the equation?

A5) i am unsure of this answer

Q6) find the greatest height that the dolphin reaches during its leap.

A6) i am unsure of this answer

2. Originally Posted by Rhyse
Q2) what horizontal distance does the dolphin cover when it first reaches a height of 25cm?

A2) 0.25=-0.4 d^2 + 2
0.25 + 0.4 = d^2 + d
0.65=d^2 +2
square root of 0.65=d + d
0.81= d+d
0.81/2=d
0.405m =d
You want to find d such that:

$0.25=-0.4d^2+2d$

rearrange:

$0.4d^2-2d+0.25=0$

which is a quadratic which you should solve using either the completing the square method or the quadratic formula, and assuming this has two positive roots you require the smaller of them. Q3 then askes for the other root.

RonL

3. Originally Posted by Rhyse
the equation is h=-0.4 d^2 + 2d.

h=height above water, d=horizontal distance.

Q4)what horizontal distance does the dolphin cover in one leap? (hint:what is the value of h when the dolphin has completed the leap?)

A4) i am unsure of this answer
The question is asking you for the horizontal distance to the point at which the dolphin reenters the water.

The dolphin enters/leaves the water when $h=0$, so you need to find $d>0$ so that:

$-0.4 d^2 + 2d=0$

which may be factorised to give:

$d(-0.4d+2)=0$

so the dolphin leaves the water when $d=0$ and re-enters the whater when $(-0.4d+2)=0$

RonL

4. Originally Posted by Rhyse
the equation is h=-0.4 d^2 + 2d.

h=height above water, d=horizontal distance.

Q5) can this dolphin reach a height of:
a)0.5 m
b)1 during a leap?
How can you work this out without actually solving the equation?

A5) i am unsure of this answer
How high is the dolphin when $d=1$?

RonL