Question

Ying is a professional deep water free diver.

His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by:
D(x)=\dfrac{1}{36}(x-60)^2-100D(x)=
36
1
​
(x−60)
2
−100D, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 36, end fraction, left parenthesis, x, minus, 60, right parenthesis, squared, minus, 100
What is the lowest altitude Ying will reach?

Answer 1

Given expression

• y=1/36(x-60)²-100

Compare to the vertex form

• y=a(x-h)²+k

We get

.

• a=1/36
• (h,k)=vertex=(60,-100)

As a is positive parabola is opening upwards and vertex is minimum

Lowest altitude is -100m

Answer 2

The lowest point is -100 meters, or 100 meters down

Explanation:

D(x)=1/36(x-60)^2-100

This equation is in vertex form

y = a(x-h)^2 +k where (h,k) is the vertex

Since a is positive, the parabola opens up

The vertex is the minimum, which means it will be the lowest point

The vertex is (60,-100)

The lowest point is -100 meters, or 100 meters down