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.

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?

The answer I received was:

h=-(x-6)^2+64

Answer 1

To solve this problem, you need to know the vertex form of a parabola:

h(t)= a(x - v_x)² + v_y, where (v_x, v_y) is the vertex and "a" is a constant. Height is a function of time.

The problem gives two points (6, 64), the vertex and (14, 0).

h(t)= a(x - 6)² + 64

To find "a", plug in the values of the second point and solve for "a":

0 = a(14 - 6)² + 64

0 = a8² + 64

0 = 64a + 64

-64 = 64a

a = -64/64 = -1

ANSWER: h(t)= -(x - 6)² + 64