Question

Abdullah is kicking a soccer ball into the air. The path of the soccer ball can be modeled by a quadratic equation where the point (6, 12) represents the vertex and the x-axis represents the ground. Which equation could represent the location of the soccer ball when it hits the ground? A 0=−(x−6)2+12 B 0=−(x+6)2−12 C 0=−(x−6)(x−12) D 0=−(x+6)(x+12)

Answer 1

9514 1404 393

Answer:

A. 0 = −(x−6)^2+12

Explanation:

The vertex form of a quadratic equation is ...

y = a(x -h)² +k . . . . . . for vertex (h, k) and scale factor 'a'

When the given vertex (h, k) = (6, 12) is used, we find the form of the equation to be ...

y = a(x -6)² +12

The ball will be on the ground when y = 0. Here, the vertical scale factor 'a' is -1, so the equation representing the ball being on the ground is ...

0 = -(x -6)² +12 . . . . . . matches choice A