Question 1078140: Please help me solve this word problem?
A frog leaps from a 1-foot high stump by a pond to land on a lily pad. When he leaps, an equation that describes his height above the pond f(×)=-0.25x^2+0.75+1, with x representing the horizontal distance from the base of the stump (directly beneath the frog). The measurements for x and are in feet. Remember that this is a mathematical frog and stump, so you do not have to take in consideration the space that each occupies.
1. What common curve would the graph of this equation be? What are the (x, y) coordinates of the frog’s initial position?
2. How far is the lily pad from the base of the stump?
3. If the frog catches a fly at the highest point of his jump, how high was the fly above the pond?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! (0,1) is the initial coordinate, and this is a parabola, convex upward.
f(×)=-0.25x^2+0.75x+1
0.25x^2-0.75x-1=0 when the frog hits the lily pad
x^2-3x-4=0
(x-4)(x+1)=0
x=4 as only positive root. The frog lands 4 feet away.
The height is the vertex with x-value -b/2a=3/2=1.5
f(1.5)=1.5625, substituting 1.5 for x in the original equation. The frog was 1.5625 feet high, or 0.5625 feet above the stump.
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