Question

A video game producer is using the quadratic function f(x) = 4 - x^2 to model the path of an arrow shot by a game player. The point (2,3) represents the top of the castle wall.
If the player moves so that the arrow will clear the wall at the maximum height, what is the new function that the game producer would need to use. Explain.

Answer 1

I know we need to have a horizontal shift. f(x+k)
Just can't figure out how to solve it.

Answer 2

First work out where the maximum of this function occurs

Answer 3

@jim_thompson5910 could you help?

Answer 4

Yes - that is what I wanted @studygeek15 to calculate.

You are also given the coordinates of the top of the wall as (2,3), so draw that in and then work out how to adjust the parabolar to that its max occurs above the wall

Answer 5

This is a better graph.
https://www.desmos.com/calculator/evuvxcssne

Answer 6

I knew what the original graph looks like. The vertex of the new graph has to be above (2,3), so the vertex should be (2,4) on the new graph. I dont understand how to work it out where the parabola's vertex would be at (2,4). I know its a horizontal shift of 2 units to the right.

Answer 7

If you shift a function \(f(x)\) by \(h\) units to the right, then it becomes \(f(x-h)\)

Answer 8

You might find this useful: http://www.mathsisfun.com/sets/function-transformations.html

Answer 9

I've tried it several times using the horizontal shift formula. I get
f(x) = (4 - x^2 - 2)
f(x) = 2 - x^2
But its not right. Am I doing it right?

Answer 10

/almost/

Answer 11

what you need to do is to replace every \(x\) term with \((x-2)\)

Answer 12

so what you should get is:\[f(x)=4-(x-2)^2\]

Answer 13

Oh okay. That's where I was getting confused. I didn't realize you replace x with x-2 Thank you for your help.

Answer 14

Would I need to go on and expand the (x-2)^2. Where my final answer would be -x^2 + 4x?

Answer 15

yes indeed - good work! :)