Question

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 1

Answer:

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

Step-by-step explanation:

Given

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

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

This gives:

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

Expand Bracket

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

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

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

Collect Like Terms

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

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

Hence, the new function is:

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

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