Question

The function y = -0.03(x - 14)^2 + 6 models the mump of a red kangaroo where x is the horizontal distance in meters and y is the vertical distance in meters for the height of the jump. What is the kangaroo's maximum height? How long is the kangaroo's jump?

Answer 1

Answer:

Kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Step-by-step explanation:

Given :$y = -0.03(x - 14)^2 + 6$

To Find : What is the kangaroo's maximum height? How long is the kangaroo's jump?

Solution:

$y = -0.03(x - 14)^2 + 6$

x is the horizontal distance in meters

y is the vertical distance in meters for the height of the jump.

Substitute y = 0

$0 = -0.03(x - 14)^2 + 6$

$0.03(x - 14)^2 = 6$

$(x - 14)^2 = \frac{6}{0.03}$

$(x - 14)^2 =200$

$(x - 14) =\sqrt{200}$

$(x - 14) =14.142$

$x =14.142+14$

$x =28.142$

x≈ 28 m

Now the maximum height will be attained at mid point i.e. $\frac{28}{2} =14$

Now substitute x= 14

$y = -0.03(14 - 14)^2 + 6$

$y = 6$

So, kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Answer 2

The trick here is to find the vertex for its highest point and find the root that is of the greatest value for the final distance.

The nice thing about this function is that it has been written in what we call vertex form. This means that the maximum (or minimum if the parabola opens upwards) is given to us at the end of the function. In this case it is 6. We know that the graph starts at (0,0) (because the cangaroo jumps starting at no height with no distance so far) and so if the x-value given for the vertex is 14, we know that if we double that value, it will give us the second root. The total distance jumped is 28m.

Highest point: 6m
Total distance: 28m