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svet-max [94.6K]
3 years ago
10

Which of the following statements describe the graphs of the solution set flr this inequality select two that apply

Mathematics
1 answer:
Helga [31]3 years ago
7 0

Answer:

1st . The shaded region of the graph ....

2nd. The graph line is solid.

4th. The ordered pair (2 ; 5) is part of the solution set.

Step-by-step explanation:

. Because y is <u>greater</u> or equal than the line, everything above the line is part of the solution.

. Since y is greater or<u> equal</u>, the line is solid. If y was only greater the line would have been dotted.

. The pair (2 ; 5) represent the x = 2 w/ y = 5, and reading the graph you can see the at this point the lines passes through it.

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Finding the equation of a parabola is quite difficult but under certain cicumstances we may easily find an equation. Let's place the focus and vertex along the y axis with the vertex at the origin. Suppose the focus is at (0,p). Then the directrix, being perpendicular to the axis, is a horizontal line and it must be p units away from V. The directrix then is the line y=-p. Consider a point P with coordinates (x,y) on the parabola and let Q be the point on the directrix such that the line through PQ is perpendicular to the directrix. The distance PF is equal to the distance PQ. Rather than use the distance formula (which involves square roots) we use the square of the distance formula since it is also true that PF2 = PQ2. We get

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Although we implied that p was positive in deriving the formula, things work exactly the same if p were negative. That is if the focus lies on the negative y axis and the directrix lies above the x axis the equation of the parabola is

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Another situation in which it is easy to find the equation of a parabola is when we place the focus on the x axis, the vertex at the origin and the directrix a vertical line parallel to the y axis. In this case, the equation of the parabola comes out to be

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