The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 12 feet, represented by a v ertex of (8,12) , and lands 16 feet from the water jet, represented by (16,0) . Write a function in vertex form that models the path of the stream
2 answers:
Answer:
y=-3/16(x-8)^2+12
Step-by-step explanation:
Refer to the vertex form equation for a parabola:
y=a(x-h)^2+k where (h,k) is the vertex.
Therefore, we have y=a(x-8)^2+12 as our equation so far. If we plug in (16,0) we can find a:
0=a(16-8)^2+12
0=64a+12
-12=64a
-12/64=a
-3/16=a
Therefore, your final equation is y=-3/16(x-8)^2+12
Answer:
y = (-5.33)(x - 8)^2 + 12
Step-by-step explanation:
The graph is a parabola which opens down and has its vertex at (8, 12). We can immediately write y = a(x - 8)^2 + 12, knowing that if x = 8, y = 12. To find the coefficient '1', substitute 16 for x and 0 for y:
0 = a(16 - 8)^2 + 12, or
-64a = 12, or a = -64/12 = 5.33
Then the desired function is:
y = (-5.33)(x - 8)^2 + 12
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