SOLUTION: A frog jumps from a rock to the shore of a pond. Its path is given by the equation:y = -5/72x^2+5/3x , where x is the horizontal distance in inches, and y is the height in inches.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A frog jumps from a rock to the shore of a pond. Its path is given by the equation:y = -5/72x^2+5/3x , where x is the horizontal distance in inches, and y is the height in inches.      Log On


   

Question 964089: A frog jumps from a rock to the shore of a pond. Its path is given by the equation:y = -5/72x^2+5/3x , where x is the horizontal distance in inches, and y is the height in inches. What is the frog’s maximum height? How far had it traveled horizontally when it reached its maximum height?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28-5%2F72%29x%5E2%2B%285%2F3%29x
By letting y=0, we can find the horizontal distance at the start (0 in traveled) and the end of the jump:
0=%28-5%2F72%29x%5E2%2B%285%2F3%29x
0=x%5E2-24x
0=x-24
24=x
The frog traveled 24 inches to the shore.
The maximum height would be mid way, when x=12 in, so
ANSWER 1: Maximum height at 12 inches horizontal distance.
y=%28-5%2F72%29%2812in%29%5E2%2B%285%2F3%29%2812in%29
y=%28-5%2F72%29%28144%29%2B%2860%2F3%29
y=%28-10%29%2B%2820%29
y=10in
ANSWER 2: Maximum height was 10 inches.
This graph is sort of a picture of the jump:
+graph%28+800%2C+400%2C+0%2C+24%2C+0%2C+11%2C+%28-5%2F72%29x%5E2%2B%285%2F3%29x%29