Question

1. A hammock is suspended between two trees. The curve the hammock makes can be modelled by the equation, y = 0.2x2 – 0.4x – 0.6, where x and y are measured in meters. (Application)

a. What do the x-intercepts tell you?

b. Does the y-intercept have any meaning in this situation.

Answer 1

Explanation:

Given that:

The modeled equation y = 0.2x² - 0.4x - 0.6

To find x- intercepts

y = 0.2x² - 0.4x - 0.6

y = 0.2(x² - 2x - 3)

y = 0.2(x - 3)(x + 1)

Suppose the upward parabola cuts x axis at x = 3 and x = - 1

Then, the length of the intercepts will be = 3 -(-1)

=4

We can say that the trees will be 4 unit apart.

To find y-intercepts;

y = 0.2(0)² - 0.4(0) -0.6

y = -0.6 meters