You are watering a garden. The height h (in feet) of water spraying from the garden hose can be modeled by h(x)=−0.1x2+0.7x+3, where x is the horizontal distance (in feet) from where you are standing. You raise the hose so that the water hits the ground 1 foot farther from where you are standing. Write a function that models the new path of the water.

Answer:

[tex]g(x) = -0.1x^2 + 0.5x + 3.6[/tex]

Step-by-step explanation:

Given

[tex]h(x) = -0.1x^2 + 0.7x + 3[/tex]

Required

Determine the new function

From the question, we understand that the new function wants the water to hit the ground 1 ft farther.

1 ft farther implies x + 1

So, in the given function, we substitute x + 1 for x in [tex]h(x) = -0.1x^2 + 0.7x + 3[/tex]

This gives:

[tex]h(x + 1) = -0.1(x + 1)^2 + 0.7(x + 1) + 3[/tex]

Expand Bracket

[tex]h(x + 1) = -0.1(x + 1)(x + 1) + 0.7(x + 1) + 3[/tex]

[tex]h(x + 1) = -0.1(x^2+2x+1) + 0.7(x + 1) + 3[/tex]

[tex]h(x + 1) = -0.1x^2-0.2x-0.1 + 0.7x + 0.7 + 3[/tex]

Collect Like Terms

[tex]h(x + 1) = -0.1x^2-0.2x + 0.7x + 0.7 + 3-0.1[/tex]

[tex]h(x + 1) = -0.1x^2 + 0.5x + 3.6[/tex]

Hence, the new function is:

[tex]g(x) = h(x + 1) = -0.1x^2 + 0.5x + 3.6[/tex]

[tex]g(x) = -0.1x^2 + 0.5x + 3.6[/tex]

The new model for path of water will be, [tex]h(x+1)=-0.1x^{2} +0.5x+3.6[/tex]

To understand more, check below explanation.

The height h (in feet) of water spraying from the garden house can be modeled by,

                 [tex]h(x)=-0.1x^{2} +0.7x+3[/tex]

where x is the horizontal distance (in feet) from where you are standing.

Since, you raise the hose so that the water hits the ground 1 foot farther from where you are standing.

So that, new function will be,

              [tex]h(x+1)=-0.1(x+1)^{2} +0.7(x+1)+3\\\\h(x+1)=-0.1(x^{2} +2x+1)+0.7x+0.7+3\\\\h(x+1)=-0.1x^{2} -0.2x-0.1+0.7x+0.7+3\\\\h(x+1)=-0.1x^{2} +0.5x+3.6[/tex]

Learn more about the function here:

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