The directrix of a parabola is y=−4y=−4 . The focus of the parabola is (−2,−2)(−2,−2) .
1 answer:
Refer to the diagram shown below.
The directrix is y = -4 and the focus is (-2, -2).
Therefore the vertex is at (-2, -3).
Consider an arbitrary point (x,y) on the parabola.
The square of distance from the focus to the point is
(x+2)² + (y+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer:
The directrix is y = -4 and the focus is (-2, -2).
Therefore the vertex is at (-2, -3).
Consider an arbitrary point (x,y) on the parabola.
The square of distance from the focus to the point is
(x+2)² + (y+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer:
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Choice A) x and f(x) approach negative infinity
Choice D) x and f(x) approach positive infinity
Step-by-step explanation:
A cubic curve starts low and ends high if the leading coefficient is positive, which in this case it is. This means that the left side of the graph falls while the right side rises. Your teacher might say something like "fall to the left, rise to the right" to describe what the end behavior is doing.
More formally "fall to the left" means that as x approaches negative infinity, y = f(x) is approaching negative infinity as well. Similarly, "rise to the right" indicates that as x approaches infinity, y = f(x) heads off to infinity as well. Both x and y = f(x) move in the same direction along their respective number lines; eg, if one goes in the negative direction, then so does the other.
The graph below confirms the answer visually.
