The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 12 feet, represented by a vertex 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

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

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

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

can you post the graph?