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)

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  A.  0 = −(x−6)^2+12

Step-by-step 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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!