Question

MODELING REAL LIFE A flare is launched from a

boat and travels in a parabolic path until reaching the
water. Write a quadratic function that models the path
of the flare with a maximum height of 300 meters,
represented by a vertex of (59, 300), landing in the
water at the point (119, 0).

Answer 1

We can start by using the vertex form of a quadratic function:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We know that the vertex is (59, 300), so we can plug in these values:

f(x) = a(x - 59)^2 + 300

To determine the value of "a", we can use the fact that the parabola passes through the point (119, 0). So we substitute these values for x and y and solve for "a":

0 = a(119 - 59)^2 + 300

-300 = 3600a

a = -1/12

Substituting this value of "a" back into the equation for f(x), we get:

f(x) = (-1/12)(x - 59)^2 + 300

This quadratic function models the path of the flare, with a maximum height of 300 meters at the vertex (59, 300), and landing in the water at the point (119, 0).