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You are watering a garden. The height $h$ (in feet) of water spraying from the garden hose can be modeled by $h\left(x\right)=-0.1x^2+0.7x+3$ , 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.

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Answer:

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

Step-by-step explanation:

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

Where h(x) is the height and x is the distance from where you are standing

The new distance is "1 foot farther from where you are standing" -- so this affects x, which becomes "x+1".

We simply replace x with x +1 in the equation of h(x) and simplify if possible:

[tex]h(x)=-0.1(x+1)^2+0.7(x+1)+3\\h(x)=-0.1(x^2+2x+1)+0.7x+0.7+3\\h(x)=-0.1x^2-0.2x-0.1+0.7x+3.7\\h(x)=-0.1x^2+0.5x+3.6[/tex]

THis is the new function.

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