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, w

Question

3 months ago

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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(x)=−0.1x2+0.7x+3, w

here 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.

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-02-28T15:07:04+03:00

Answer:

$g(x) = -0.1x^2 + 0.5x + 3.6$

Step-by-step explanation:

Given

$h(x) = -0.1x^2 + 0.7x + 3$

Required

Find the updated function

The problem specifies that the water should land 1 ft further away.

This means we need to use x + 1

Consequently, in the initial function, we will replace x with x + 1 in $h(x) = -0.1x^2 + 0.7x + 3$

Thus, we obtain:

$h(x + 1) = -0.1(x + 1)^2 + 0.7(x + 1) + 3$

Expand the Parenthesis

$h(x + 1) = -0.1(x + 1)(x + 1) + 0.7(x + 1) + 3$

$h(x + 1) = -0.1(x^2+2x+1) + 0.7(x + 1) + 3$

$h(x + 1) = -0.1x^2-0.2x-0.1 + 0.7x + 0.7 + 3$

Combine Like Terms

$h(x + 1) = -0.1x^2-0.2x + 0.7x + 0.7 + 3-0.1$

$h(x + 1) = -0.1x^2 + 0.5x + 3.6$

The resulting function is:

$g(x) = h(x + 1) = -0.1x^2 + 0.5x + 3.6$

$g(x) = -0.1x^2 + 0.5x + 3.6$