# how do i find the answer

*label*Mathematics

*timer*Asked: May 15th, 2015

*account_balance_wallet*$5

### Question Description

A coordinate grid is mapped on a video game screen, with the origin in the lower-left corner. A game designer programs a helicopter to follow a path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25). She also programs an airplane to move along a linear path that passes through the points (0, 18) and (30, 20). Which system of equations can be used to determine whether the paths of the helicopter and airplane cross?

## Tutor Answer

1. " linear path that passes through the points (0, 18) and (30, 20)".

The equation of this line is (x-0)/(30-0) = (y-18)/(20-18), or

x/30 = (y-18)/2.

2. "path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25)"

I suppose that they speak about vertical parabola. The equation is y = a*x^2 + b*x + c.

The vertex has coordinates (-b/2a, c-b^2/(4a)) = (16, 20).

Parabola passing through (4, 25) means 25 = a*4^2 + b*4 + c.

There are 3 equations on a,b,c and we have to solve this system.

(I'll show the solution later because 20 min are insufficient)

3. "video game screen, with the origin in the lower-left corner" means x>=0, y>=0 and x<width of the screen, y<height of the screen.

Also, x and y may be non-integer but for screen we need the nearest integers of the exact solution.

So the system is:

x/30 = (y-18)/2,

y = a*x^2 + b*x + c (a, b, c are constants we have to find before)

and x>=0, y>=0, x<W, y<H.

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