Question

Task 3:
A frog sitting on a stump 4 feet high hops off and lands on
the ground. During her leap, the frog's height h in feet is
given by the equation h = -0.5d2 + d + 4, where d is the
horizontal distance in feet from the base of the stump.
A: What was the frog's maximum height?
B: How far from the stump did the frog land?
C: What was the frog's horizontal distance
from the log at her maximum height?

Answer 1

Answer:

A.   4.5 ft

B.    4 ft

C.    1 ft

Step-by-step explanation:

If you pretend that h is replacing y and d is replacing x and you would graph the equation, then you would get a parabola that opens down.

You would need to find the vertex of the parabola.  The ordered pairs would be (d, h) instead  of the normal (x, y).  

A.  The maximum height will be the h value of the vertex

B.   Let h = 0 and solve the equation for d.  That will give you distance from the stump that the frog landed.

C.  The distance from the log at the maximum height is the d value of the vertex

So, that is what is needed to be done.

Without me going thru all the work, the vertex is (1, 4.5) and the solutions to the equation when h = 0 are 4, -2  (discard -2 since a distance cannot be negative)

So the answer to A is 4.5 ft.

The answer to B is 4ft.

The answer to C is 1 ft.

Now, can you find the vertex on your own and can you solve the equation when h = 0?  I hope so.  OK?

Answer 2

A function assigns the values. The maximum height will be when the horizontal distance is 1feet from the log.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

A.) The maximum height of the frog,

h = -0.5d²+d+4

dh/dd = -0.5(2d)+1

dh/dd = -d+1

0=-d+1

d = 1

The maximum height will be when the horizontal distance is 1feet from the log.

h = -0.5(1)² + 1 + 4

h = -0.5 + 1 + 4

h = 4.5

Hence, the maximum height of the frog will be 4.5 feet.

B.) The Distance between the frog and the stump when the frog land can be found,by putting h=0.

0 = -0.5(d)²+ d + 4

d²-2d-8=0

d²-4d+2d-8=0

d(d-4)+2(d-4)=0

d = 4, -2

Since the distance can not be negative, the frog is 4 feet away from the stump when the frog land.

C.) The maximum height will be when the horizontal distance is 1feet from the log.

Learn more about Function:

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