Question

A ball is dropped from a height of 4.05 meters above the ground. So, 4.05 meters is the ball's maximum height. After 0.5 seconds, the ball is 2.8 meters above
the ground. The ball hits the ground 0.9 seconds after it is dropped.
Let f (x) be the height (in meters) of the ball x seconds after it is dropped. Then, the function fis quadratic. (Its grach is a parabola with vertex (0, 4.05).)
Write an equation for the quadratic function.

Answer 1

Answer:

y = -5x² + 4.05

Explanation:

Equation of a parabola is:

y = a (x − h)² + k

where (h, k) is the vertex.

Given that the vertex is (0, 4.05):

y = a (x − 0)² + 4.05

y = ax² + 4.05

Use any of the other points provided to solve for a. At x = 0.9, y = 0.

0 = a (0.9)² + 4.05

0 = 0.81a + 4.05

0.81a = -4.05

a = -5

Therefore, the quadratic equation is:

y = -5x² + 4.05