Question

Stellan, an alien from the planet Tellurango, shoots a flaming projectile straight up into the air from the edge of a cliff that is 28 meters high. According to the laws of physics on his planet, the height of the projectile, h, after t seconds is modeled by a quadratic equation. The projectile reaches a maximum height of 64 meters after 6 seconds, and the projectile is airborne for 14 seconds. In other words, after 14 seconds, the projectile has a height of 0 meters because it is on the ground. What is the vertex form of the quadratic equation that represents the height, h, of the projectile after t seconds?

Answer 1

The required equation is h(t)= -(x - 6)² + 64.

Explanation:

Consider the provided information.

The vertex form of a parabola is:

f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

The projectile reaches a maximum height of 64 meters after 6 seconds, According to the laws of physics on his planet, the height of the projectile, h, after t seconds is modeled by a quadratic equation.

The quadratic equation has maximum height h = 64 after t = 6 second.

Thus, the vertex of the parabola is (6,64)

Use the above vertex form to find the equation of parabola.

f(x) = a(x - 6)² + 64

It is given that after 14 seconds, the projectile has a height of 0 meters.

Thus, the second point is (14,0)

Now to find the value of "a", Substitute the values of the second point in above equation and solve for "a".

0 = a(14 - 6)² + 64

0 = a(8)² + 64

0 = 64a + 64

-64 = 64a

a = -1

Hence, the required equation is h(t)= -(x - 6)² + 64.