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Question:

A ball is dropped from a height of $18$ metres. The quadratic equation $h = -2t^2 + 18$ gives you the height, $h$ metres, of the ball, after $t$ seconds.

After how many seconds does the ball hit the ground?

What I've tried so far: I have tried rearranging the equation but that just got me to a dead end. I was thinking of tried to complete the square or factorising but I am not entirely sure. Thanks for your help.

Ivan Neretin
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Hanka
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2 Answers2

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Hint: we're given a polynomial of degree 2, with a negative constant infront of the t^2 term. What would a graph of this function look like?

  • If it's negetive, will the graph be flipped upside down in terms of $-x^2$? I'm not sure... – Hanka Jun 04 '16 at 12:23
  • Good! Now we're given h=8, so plug that in, and combine like terms. Plug it into a graphing application/calculator. What is the importance of the roots/zeroes? –  Jun 04 '16 at 12:28
  • Oopsy... Typo. I meant $h=18$. @RonaldB – Hanka Jun 04 '16 at 12:32
  • @Hanka did you figure out what the importance of the zeroes is? Doesn't really matter what $h$ is. –  Jun 04 '16 at 12:33
  • Should I try to plug 0 into the equation and rearrange with like terms from there? @RonaldB – Hanka Jun 04 '16 at 12:42
  • Is $t = 3$ by any chance? – Hanka Jun 04 '16 at 12:43
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Hint: the ball hits the ground means that $h=0$, how does this simplify our equation?

amiz9
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