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?

• From the vertex of the quadratic equation, we find that: The kangaroos maximum height is of 6 meters.

• From the roots of the equation, we find that: The kangaroo's jump is 28.14 meters long.

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Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

Where

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is .

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Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

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The quadratic equation is:

Placing in standard form:

Thus, it has coefficients

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The kangaroo's maximum height is the y-value of the vertex, thus:

The kangaroos maximum height is of 6 meters.

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The length of the kangaroo's jump is the positive root. The roots are found at the values of x for which y = 0, thus, the solutions of the quadratic equation.

The kangaroo's jump is 28.14 meters long.

A similar question is given at brainly.com/question/16858635

Answer:

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

Step-by-step explanation:

Given :

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

Solution:

x is the horizontal distance in meters

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

Substitute y = 0

x≈ 28 m

Now the maximum height will be attained at mid point i.e.

Now substitute x= 14

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