There is an arcade in the amusement park. A computer game there uses functions to simulate the paths of an archer’s arrows. The
x-axis represents the level ground on which the archer stands, and the coordinate pair (2,5) represents the top of a castle wall over which he is trying to fire an arrow.
In response to user input, the first arrow followed a path defined by the function f(x)=6-x^2, failing to clear the castle wall.
The next arrow must be launched with the same force and trajectory, so the user must reposition the archer in order for his next arrow to have any chance of clearing the wall.
a. How much closer to the wall must the archer stand in order for the arrow to clear the wall by the greatest possible distance?
b. What function must the user enter in order to accomplish this?
c. If the user can only enter functions of the form f(x+k), what are all the values of k that would result in the arrow clearing the castle wall?
In response to user input, the first arrow followed a path defined by the function f(x)=6-x^2, failing to clear the castle wall.
The next arrow must be launched with the same force and trajectory, so the user must reposition the archer in order for his next arrow to have any chance of clearing the wall.
a. How much closer to the wall must the archer stand in order for the arrow to clear the wall by the greatest possible distance?
b. What function must the user enter in order to accomplish this?
c. If the user can only enter functions of the form f(x+k), what are all the values of k that would result in the arrow clearing the castle wall?
1 answer:
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Answer:
x = -1, x = 1
Step-by-step explanation:
Factor the equation. (It's a difference of squares, so we know the form will be (a-b)(a+b).)
Test this by FOILing it out, if you're unsure. This is something it can be good to memorize!
Set it equal to 0.
Separate the two parenthetical expressions by the Zero Product Property.
Solve for x!