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