d=4

 

∴ when the basketball is 8m high it will travel 4m far, because you cannot throw a basketball into the air and have it go 0m far, that is impossible, so ∴ 4m is the answer.

 

 

2. A magical dolphin jumping out of the water is modelled by the equation y=(x+3)(x+6), where x=how long the magical dolphin is out of the water for(in s) , and y=how high the magical dolphin jumps vertically(in m).

How high will the magical dolphin be out of the water when it is 2s out of it?

 

Answer: Substitute 2 into x...

y=(2+3)(2+6)

 

Add everything in the brackets...

y=(5)(8)

 

Multiply...

y= 40m

 

 

∴ The magical dolphin will be 40m high when it is 2s out of the water.

 

 

3. An arch shaped bridge is being built in between San Francisco and The Pacific Ocean is modelled by the equation y=-0.2(x-5)^2+1. The bridge is measured in km.

a) How high is the bridge?

 

Answer: The answer is the optimal value(k), ∴ the bridge is 1km high.

 

b)How long will the road be in between San Francisco and The Pacific Ocean?

 

Answer: First solve the x-intercepts...

y=-0.2(x-5)^2+1

0=-0.2(x-5)^2+1

-0.2(x-5)^2+1=0

-0.2(x-5)^2=1

(x-5)^2=1/0.2

x-5=√5

x=5±2.2360679775

x=7.2360679775

x=2.7639320225

 

Once you have those simply subtract them...

7.2360679775-2.7639320225(The lower number is always subtracted by the higher number for this type of question)

=4.472135955

 

∴ the road between San Francisco and The Pacific Ocean will be approximately 4.47km long.