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While watering her outdoor plants, Maura noticed that the water coming out of her garden hose followed a parabolic path. Thinking that she might be able to model the path of the water with an equation, she quickly took some measurements. The highest point the water reached was 8 feet, and it landed on the plants 10 feet from where she was standing. Both the nozzle of the hose and the top of the flowers were 4 feet above the ground. Help Maura write an equation that describes the path of the water from the hose to the top of her plants. You may Desmos to help come up with your answer.


Using the equation y=a(x−h)2+k

find the values of each,

A=

H=

K=

Respuesta :

According to the information given, the parabolic equation which describes the path of the water from the hose to the top of her plants is:

  • [tex]y = -\frac{1}{9}(x - 10)^2 + 8[/tex]
  • The coefficients are [tex]a = -\frac{1}{9}, h = 10, k = 8[/tex].

What is the equation of a parabola?

The equation of a parabola, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In this problem:

  • The highest point the water reached was 8 feet, and it landed on the plants 10 feet from where she was standing, hence the vertex is (10,8), that is, [tex]h = 10, k = 8[/tex].

Then:

[tex]y = a(x - 10)^2 + 8[/tex]

Both the nozzle of the hose and the top of the flowers were 4 feet above the ground, hence point (4,4), when [tex]x = 4, y = 4[/tex] is part of the function, which is used to find a.

[tex]y = a(x - 10)^2 + 8[/tex]

[tex]4 = a(4 - 10)^2 + 8[/tex]

[tex]36a = -4[/tex]

[tex]a = -\frac{4}{36}[/tex]

[tex]a = -\frac{1}{9}[/tex]

Hence, the equation is:

[tex]y = -\frac{1}{9}(x - 10)^2 + 8[/tex]

You can learn more about equation of a parabola at https://brainly.com/question/26144898

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