Let point (x, y) be any point on the graph, than the distance between (x, y) and the focus (3, 6) is sqrt((x - 3)^2 + (y - 6)^2) and the distance between (x, y) and the directrix, y = 4 is |y - 4|
Thus sqrt((x - 3)^2 + (y - 6)^2) = |y - 4|
(x - 3)^2 + (y - 6)^2 = (y - 4)^2
x^2 - 6x + 9 + y^2 - 12y + 36 = y^2 - 8y + 16
x^2 - 6x + 29 = -8y + 12y = 4y
(x - 3)^2 + 20 = 4y
y = 1/4(x - 3)^2 + 5
Required answer is f(x) = one fourth (x - 3)^2 + 5
the cost of one soccer ball is 150/6 or 25 dollars.
First question:
I urge you to perform the division using the synthetic division method:
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-4 / 1 3 -6 -6 8
-4 4 8 -8
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1 -1 -2 2 0
Note that there is no remainder. When this is the case, the divisor (here, that's -4) is a root of the given polynomial, and the value of that polynomial, g(-4), is 0.
If the remainder were not 0, then the remainder represents the value of the polynomial for that particular divisor. For example, if x = -3, the remainder is -28. We'd write that as g(-3) = -28.
But here, g(-4) = 0.
The expressions have the same expansion I'd say because the pairs 2 and 30, 3 and 20, and 4 and 15 because they are all equivalent to 60 because they are all factors of 60.
Same goes with the other pairs, because they are all equivalent to 48 because they are all factors of 48.
20 = 8 + v equals v = 12.
First, subtract 8 from both sides. Your problem should look like: 20 - 8 = v
Second, simplify 20 - 8 to get 12. Your problem should look like: 12 = v.
Third, switch sides to get v = 12, which is the correct answer.
