Question

Sam is sitting in a boat on a lake. She can get sunburned from the sunlight that hits her directly and from
sunlight that reflects off the water. Sunlight reflects off the water at the point (4,0) and hits Sam at the
point (5.5,3). Enter the function that describes the path of the sunlight in the form y =alx - h|+k, then
select the graph of the function. Round each value in the equation to 2 decimal places.
y =

Answer 1

An absolute function is represented as: $y = a|x - h| + k$ where the vertex is (h,k).

The function that describes the path of the sunlight is: $y= 2|x - 4|$

We have:

$(h,k) = (4,0)$ --- the vertex i.e. the point where the sun hits the water

$(x,y) =(5.5,3)$

Recall that:

$y = a|x - h| + k$

Substitute $(h,k) = (4,0)$

$y = a|x - 4| + 0$

$y = a|x - 4|$

Substitute $(x,y) =(5.5,3)$ to solve for a

$3 = a|5.5 - 4|$

$3 = a|1.5|$

Take absolute value of 1.5

$3 = 1.5a$

Solve for a

$a = \frac 3{1.5}$

$a = 2$

Recall that:

$y = a|x - 4|$

Substitute $a = 2$

$y= 2|x - 4|$

Hence, the function that describes the path of the sunlight is: $y= 2|x - 4|$

See attachment for the graph of $y= 2|x - 4|$

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