Antoine Stands On A Balcony And Throws A Ball To His Dog, Who Is At Ground Level., "The Balls Height (In Meters Above The Ground), Xxx Seconds After A

Antoine stands on a balcony and throws a ball to his dog, who is at ground level.

The balls height (in meters above the ground), xxx seconds after Antoine threw it, is modeled by:
h(x)=-2x^2+4x+16h(x)=−2x
2
+4x+16h, left parenthesis, x, right parenthesis, equals, minus, 2, x, start superscript, 2, end superscript, plus, 4, x, plus, 16
How many seconds after being thrown will the ball hit the ground?

 

Answer:

The ball hit the ground after 4 seconds.

Step-by-step explanation:

Model of parabola of the ball thrown to the dog from the balcony:

h(x)=-2x²+4x+16

Where:

h(x) is the height of the ball from the balcony at x seconds

y-intercept is the height of the balcony from the ground ⇒ 16 meters

To solve for the time the ball reaches the dog on the ground, solve for x.

Set h(x) at 0 meters on ground level.

-2x²+4x+16 = 0

Factor the equation:

-2(x - 4) (x + 2) = 0

Find the x, the time in seconds:

x - 4 = 0

x = 4

x +2 = 0

x = -2

Choose the positive value for time:

The ball hit the ground after 4 seconds.


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