Question

Well I had helped quite a few students here earlier and now I wonder if some one is here to help me with this

A video game producer is using the quadratic function f(x) = 4 – x2 to model the path of an arrow shot by a game player. The path of the arrow is shown in the graph below. 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? Use complete sentences and explain your work.

Answer 1

alright, so, given a point and the "slope" could you find the eq?

Answer 2

@ganibl

Answer 3

Yes @FibonacciChick666

Answer 4

so first, at what x value is the ball at it's highest point?

Answer 5

From the graph I believe it is 2

Answer 6

not quite, so the y value represents the height, where does the function have a max?

Answer 7

at y= 4 function has maximum value

Answer 8

uhm not exactly but you have the right idea, when you reference max and mins you want to say it occurs at x= not y=

Answer 9

oh ok

Answer 10

so where is the max again?

Answer 11

x = 4 is maximum then?

Answer 12

@FibonacciChick666

Answer 13

no, what is the x value when y=4? just look at the graph, what are the coordinates of the max?

Answer 14

Ok I got it now at x = 0 it is maximum Hope this time I got it right :)

Answer 15

you did, yay! so now we have the max, but we want to change it's location, so what x value do we want the max to occur at?

Answer 16

I think it is at x = 2 which means we need to shift it two units to the right this is what I understood please guide me if I am wrong

Answer 17

yep that is the idea so what will our point for the new function be?

Answer 18

(2, 4) ?

Answer 19

good, so now we need to find the slope of our fn. Can you tell me the derivative of f(x)?

Answer 20

I believe it is -2x but we do not have derivatives discussed so far

Answer 21

oh,that sucks.... it is -2x so I mean using that you can find the answer, but let me think of another way to arrive at the same

Answer 22

alright a bit more round about but I think we get the same

Answer 23

so, we want to translate the graph two units to the right correct?

Answer 24

Yes Exactly that is what I figured out

Answer 25

I am thinking on translating equations method will help any idea on that?

Answer 26

so we want to increase the x values by 2 right?

Answer 27

Yes

Answer 28

(x + 2)^2 - 4?

Answer 29

x^2 + 4x + 4 - 4
x^2 + 4x ?

Ahh somewhere I might be wrong

Answer 30

look at the original

Answer 31

but that is my theory

Answer 32

Oops sorry I got it right now 4 - (x + 2)^2

Answer 33

alright, so let's see if that works

Answer 34

check it using the derivative and the point would be my suggestion or graph it

Answer 35

graphing is eqasier

Answer 36

Ok Thanks much for your help @FibonacciChick666

Answer 37

so it doesn't look quite right when I graph it

Answer 38

it actually went to the left, so any ideas on how to fix it?

Answer 39

So it should be 4 - (x - 2)^2

4 - x^2 + 4x - 4

x^2 - 4x ?

Answer 40

yep

Answer 41

So is that right?

Answer 42

yup

Answer 43

Thanks @FibonacciChick666 Your help is greatly appreciated

Answer 44

np

Answer 45

:)