Answer:
The equation represents the equation of the parabola with focus (-3, 3) and directrix y = 7.
Step-by-step explanation:
To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).
Using the distance formula , we find that the distance between (x, y) is
and the distance between (x, y) and the directrix y = 7 is
.
On the parabola, these distances are equal so, we solve for y:
A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so
A dilation of 2 is the mapping (x'',y'')=(2x', 2y')
So
We can rewrite that without the primes and combine the powers of 2.
Let's graph these and see if we're close,
Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}
27 inches ......... 3/8
x inches .............8/8
<h3>x = (27×8/8)/(3/8) = 27×8/3 = 216/3 = 72 inches (father)</h3>
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