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1 answer:
<h3>Answer: Choice C. |x+3| < 5</h3>
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Explanation:
Let's go through each answer choice and solve for x
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Choice A
|x+3| < -5
This has no solutions because |x+3| is never negative. It is either 0 or positive. Therefore, it can never be smaller than -5. So we can rule this out right away.
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Choice B
|x+8| < 2
-2 < x+8 < 2 .... see note below
-2-8 < x+8-8 < 2-8 ... subtract 8 from all sides
-10 < x < -6
We will have a graph where the open circles are at -10 and -6, with shading in between. This does not fit the original description. So we can rule this out too.
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Choice C
|x+3| < 5
-5 < x+3 < 5 .... see note below
-5-3 < x+3-3 < 5-3 .... subtracting 3 from all sides to isolate x
-8 < x < 2
We found our match. This graph has open circles at -8 and 2, with shading in between. The open circles indicate to the reader "do not include this value as a solution".
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note: For choices B and C I used the rule that turns into
where k is some positive number. For choice A, we have k = -5 which is negative so this formula would not apply.
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At an arbitrary point P (x,y) on the parabola, the distance, d, from the focus to P should be equal to the distance from P to the directrix.
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Divide each side by 6 to obtain
y = (1/6) (x - 3)² + 5/2
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The line of symmetry is x = 3.
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At an arbitrary point P (x,y) on the parabola, the distance, d, from the focus to P should be equal to the distance from P to the directrix.
That is,
d² = (x - 3)² + (y - 4)² = (y - 1)²
(x - 3)² + y² - 8y + 16 = y² - 2y + 1
(x - 3)² + 15 = 6y
Divide each side by 6 to obtain
y = (1/6) (x - 3)² + 5/2
The vertex of the parabola is at (3, 5/2).
The line of symmetry is x = 3.
The leading coefficient, 1/6, is positive, therefore the curve opens upward.
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