WHY IS NOBODY ANSWERING!! PARABOLAS

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4. See explanation

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Step-by-step explanation:

1. The equation of given parabola is

The vertex of this parabola is at point (1,-3), this parabola goes in positive x-direction and has the parameter such that

The directrix is the vertical line. The equation of the directrix is

2. The vertex of the parabola is at point (-5,2), the focus is at point (-5,6), this means that the vertex and the focus both lie on the vertical line x = -5. This line is the line of symmetry of the parabola. Thus, parabola goes in positive y-direction and has the equation

To find the parameter note that the distance between vertex and focus is equal to hence,

and the equation of the parabola is

3. Given the equation

Rewrite this equation as follows

4. Given the equation of the parabola

The vertex of the parabola is at point (3,-1).

The parabola opens to the right.

Parabola's parameter is , so the focus is units away from the vertex.

The directrix is units away from the focus.

The focus is at the point and the directrix has the equation

5. The distance between the directrix and the focus is

units.

The directrix is to the right from the focus, so parabola opens to the left and has the equation

where is the vertex.

The vertex is the point that is half way from the focus to the directrix, hence

So, the equation is

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: