quadratic relation word problem

The main character in a video game, Tammy, must swing on a vine to cross a river. If she grabs the vine at a point that is too low and swings within 80cm of the surface of the river, a crocodile will come out of the river and catch her. From where she is standing on the riverbank, Tammy can reach a point on the vine where her height above the river, h, is modeled by the relation h = 6x2 - 56.8x + 228, where x is the horizontal distance from her swing from her starting point. Should Tammy jump?

Can anyone help me with solving this problem?

I think I have to use the quadratic formula, and plug in 6 for a, -56.8 for b, and c will become 228 - 80 = 148. but when I do that, I get a negative number underneath the square root sign. Since this is not possible, does this mean that she should not jump?

Any help would be great. Thanks.

Re: quadratic relation word problem

There's indeed no $\displaystyle x$ value wherefore:

$\displaystyle 80=6x^2-56,8x+228$, so that means she'll never reach the 80cm but she will always be higher then that point.

Re: quadratic relation word problem

thank you so much for your help! I really appreciate it. and you helped me make sense of the question with your help!!!!!!! and thanks for responding so quickly!!!!!!!!

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-Amanda