Question

Distance in Feet

Answer 1

9514 1404 393

Answer:

  a) y = -7/640x^2 +7/4x

  b) y = -7/640(x -80)^2 +70

Step-by-step explanation:

a) Given the equation in standard form:

  y = ax^2 +bx +c

we can use the points (0, 0), (80, 70), and (160, 0) to find the values of a, b, c.

  a·0 +b·0 +c = 0

  a·80^2 +b·80 +c = 70

  a·160^2 +b·160 +c = 0

The first equation tells us that c=0, so we can write a reduced matrix for the last two equations. The augmented matrix is ...

  $\left[\begin{array}{cc|c}6400&80&70\\25600&160&0\end{array}\right]$

A matrix solver finds the solution to be ...

  a = -0.0109375 = 7/640, b = 1.75 = 7/4

The standard-form equation for Money's path is ...

  y = -7/640x^2 +7/4x

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b) Factoring out -7/64, we have ...

  y = -7/640(x^2 -160x)

adding and subtracting the square of the x-coefficient, we have ...

  y = -7/640(x^2 -160x +6400) +70

  y = -7/640(x -80)^2 +70