SOLUTION: The main charater 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 80 cm of the surface of the riv

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The main charater 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 80 cm of the surface of the riv      Log On


   

Question 473418: The main charater 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 80 cm of the surface of the river, a crocodile will come out of the riverf and catch her. From where she is standing on the river bank, tammy can reach a point on the vine where her height above the river, h, is modelled by the relation h=6x2-56.8+228, where,x, is the horizontal distance of her swing from her starting point. Should Tammy jump?
Please show steps is crucial
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
h+=+6x%5E2+-+56.8x+%2B+228
If h ever goes below 80 then the crocodile will catch her.
Find minimum value and test to see if it is greater than 80.
Minimum value of an upward parabola is at the vertex.
To find x_coordinate of vertex, x+=+%28-b%29%2F2a where a,b,c are the coefficients 6,-56.8,228
x+=+%28-%28-56.8%29%29%2F%282%2A6%29+=+56.8%2F12+=+4.73
Now find the corresponding height at x=4.73
h+=+6%284.73%5E2%29+-+56.8%284.73%29+%2B+228
h+=+134.24+-+268.66+%2B+228
h+=+93.6
Therefore since minimum height is 93.6, at no point will she fall below 80 and it is safe to jump