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 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?

Answer 1

hang on let me attach the graph

Answer 2

is it saying that the vertex needs to be at (2, 3) instead of (0, 4)?

Answer 3

The only thing I know is that it needs to be at (2,4) since it is right above (2,3).

Answer 4

or actually I think it does have to be at (2,3).

Answer 5

I think (2, 3) because it said it's supposed to clear the wall at max height.
Use this equation for vertex form of any parabola
\[f(x) = (x - h)^2 +k\]

h = 2, the horizontal position of the vertex
k = 3, the vertical position of the vertex

Answer 6

so it would be f(x) =(x - 2)² + 3

Answer 7

yes

Answer 8

but how do I solve it? im sorry im not great at math

Answer 9

there's nothing to solve. It's only asking for the function

Answer 10

oh ok so thats the answer?

Answer 11

yes

Answer 12

thanks!

Answer 13

can you help me with another problem?

Answer 14

you're welcome. ok

Answer 15

Create a quadratic equation in standard form that can be factored.
Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.
Write your equation in factored form. Use complete sentences to explain the benefits of writing your equation in factored form.
Write your equation in vertex form. Use complete sentences to explain the benefits of writing your equation in vertex form.
Explain how all three forms can be used together to help you graph a quadratic function. Graph your function, and label the y-intercept, the x-intercepts, and the vertex.

Answer 16

that's a much longer problem. I'd start with the factored form and then foil to get the standard.

If you start with something like \(y=(x+3)(x-4)\), that's factored form, and it lets you find the x-intercepts easily by setting each factor equal to 0 and solving for x.

The FOIL the factored form equation to get the standard form equation. That lets you find the y-intercept easily by plugging in 0 for x and solving for y.

Then complete the square on the standard form equation to find the vertex form, which let's you find the vertex by picking out the h and k values like we did above.

I can't stick around to work through it, but hopefully that can get you started

Answer 17

That's fine I think I can do the rest myself but thanks for helping!