# MAC1105!, college algebra

## MAC1105!, college algebra

Can someone please solve the following quadratic function in full and in-depth explanations if possible, with the following ten corresponding and orderly steps if you do not mind please? I would hugely appreciate if anyone decided to take on this math probelm and plz asnwer it for me

f(x)=2x^2+5x+3

Step 1: vertical ine test:

Step 2: the domain:

Step 3: The range:

Step 4: the x and Y intercepts:

Step 5: is it symmetric:

Step 6: Function values:

Step 7: Intervals, increase and decrease, if any:

Step 8: turning point:

Step 9: max and min locasus:

Step 10: the vertex:

Step 11: the average rate of change:

Thank you so much and God bless you!!!

f(x)=2x^2+5x+3

Step 1: vertical ine test:

Step 2: the domain:

Step 3: The range:

Step 4: the x and Y intercepts:

Step 5: is it symmetric:

Step 6: Function values:

Step 7: Intervals, increase and decrease, if any:

Step 8: turning point:

Step 9: max and min locasus:

Step 10: the vertex:

Step 11: the average rate of change:

Thank you so much and God bless you!!!

**JFV**- Posts : 10

Join date : 2008-11-18

## Re: MAC1105!, college algebra

Step 1: vertical line test: The vertical line test - "The Vertical Line Test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once." So I guess if you draw a vertical line anywhere, you can see that it only intersects with the parabola at most at one point, so it's a function. And, it's already defined as a function anyway (f(x)=... and there isn't any weird stuff that would make it return multiple values like "+-", which is in the quadratic formula, for example)

Step 2: the domain: -infinity < x < infinity (Like all functions in the form f(x)=a*x^2+b*x+c, with a, b, and c being real number constants)

Step 4: the x and Y intercepts: Factor or use the quadratic formula to get the x intercepts, and plug evaluate f(0) to get the y intercept.

Step 5: is it symmetric: ...about the y axis? It'll be symmetric about the y axis if the coefficient of the "x" term is 0 for a quadratic function. In this case, it is 5 (because of "5x"), so it is not symmetric about the y axis.

Step 3: The range:

Step 7: Intervals, increase and decrease, if any:

Step 9: max and min locasus:

Step 10: the vertex:

Probably the "normal" way to find the vertex by completing the square to create a possibly friendlier function to work with, which in which the vertex naturally appears: a(x-b)^2+c, the vertex is at: (b,c). However, notice that in the quadratic formula, it can be slightly changed into: -b/(2a) +- sqrt(b^2-4*a*c)/(2a); one root is at -b/(2a) + sqrt(b^2-4*a*c)/(2a), the other is at -b/(2a) - sqrt(b^2-4*a*c)/(2a), the vertex is in the middle of the two roots, and occurs at x=-b/(2a). So the vertex here is at the point (-5/(2*2),f(-5/(2*2))

If the coefficient for the "x^2" term is positive, then the vertex will be at a minimum (and to the left of the vertex the function will decrease and to the right of the vertex the function will increase, and the range will be y equals that minimum and higher values), and if it's negative, then the vertex will be at a maximum (and to the left of the vertex the function will increase and to the right of the vertex the function will decrease, and the range is that maximum and lower values).

Step 11: the average rate of change: The slope? Over what interval? The slope is calculated by doing: (Y2-Y1)/(X2-X1) between the points (X1,Y1) and (X2,Y2)

Step 2: the domain: -infinity < x < infinity (Like all functions in the form f(x)=a*x^2+b*x+c, with a, b, and c being real number constants)

Step 4: the x and Y intercepts: Factor or use the quadratic formula to get the x intercepts, and plug evaluate f(0) to get the y intercept.

Step 5: is it symmetric: ...about the y axis? It'll be symmetric about the y axis if the coefficient of the "x" term is 0 for a quadratic function. In this case, it is 5 (because of "5x"), so it is not symmetric about the y axis.

Step 3: The range:

Step 7: Intervals, increase and decrease, if any:

Step 9: max and min locasus:

Step 10: the vertex:

Probably the "normal" way to find the vertex by completing the square to create a possibly friendlier function to work with, which in which the vertex naturally appears: a(x-b)^2+c, the vertex is at: (b,c). However, notice that in the quadratic formula, it can be slightly changed into: -b/(2a) +- sqrt(b^2-4*a*c)/(2a); one root is at -b/(2a) + sqrt(b^2-4*a*c)/(2a), the other is at -b/(2a) - sqrt(b^2-4*a*c)/(2a), the vertex is in the middle of the two roots, and occurs at x=-b/(2a). So the vertex here is at the point (-5/(2*2),f(-5/(2*2))

If the coefficient for the "x^2" term is positive, then the vertex will be at a minimum (and to the left of the vertex the function will decrease and to the right of the vertex the function will increase, and the range will be y equals that minimum and higher values), and if it's negative, then the vertex will be at a maximum (and to the left of the vertex the function will increase and to the right of the vertex the function will decrease, and the range is that maximum and lower values).

Step 11: the average rate of change: The slope? Over what interval? The slope is calculated by doing: (Y2-Y1)/(X2-X1) between the points (X1,Y1) and (X2,Y2)

**bfrsoccer**- Administrator
- Posts : 61

Join date : 2008-11-09

## Re: MAC1105!, college algebra

Australia to hold referendum recognising Aborigines

By Phil Mercer

BBC News, Sydney

Ms Gillard said efforts to help Aborigines could not succeed without greater respect and recognition

Continue reading the main story

Related stories

Notorious Aboriginal ghetto to be bulldozed

First Aboriginal MP for Australia

Aboriginal children 'starving'

Australia will hold a referendum on recognising its indigenous people in the constitution to improve conditions for its most disadvantaged community.

Prime Minister Julia Gillard said there was a "once-in-50-year opportunity" to harness public and parliamentary support for greater recognition.

The 550,000 Indigenous Australians make up 2.7% of the population.

They suffer disproportionately high rates of unemployment, imprisonment, drug abuse, alcoholism and disease.

'Change needed'

Ms Gillard, of the centre-left Labor party, said that practical efforts to help Australia's Aborigines and Torres Strait Islanders could not succeed without greater respect.

"The Australian constitution is the foundation document of our system of government, but it fails to recognise the special place of our first Australians," she said in a joint statement with the minister for indigenous affairs and the attorney-general.

"Constitutional recognition of Indigenous Australians is an important step towards building a nation based on strong relationships and mutual respect," she added.

"Recognition will demonstrate that we are a country that is united in acknowledging the unique and special place of our first peoples."

The referendum will ask the country to give constitutional recognition to indigenous people. It is unclear when the vote will take place.

Aboriginal leaders say a positive result would have a "dramatic effect" on the community's self-esteem.

Forty-four referendums have been held in Australia since 1901. Only eight have been passed.

_________________________________________________________________________________________________________________________________________________

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By Phil Mercer

BBC News, Sydney

Ms Gillard said efforts to help Aborigines could not succeed without greater respect and recognition

Continue reading the main story

Related stories

Notorious Aboriginal ghetto to be bulldozed

First Aboriginal MP for Australia

Aboriginal children 'starving'

Australia will hold a referendum on recognising its indigenous people in the constitution to improve conditions for its most disadvantaged community.

Prime Minister Julia Gillard said there was a "once-in-50-year opportunity" to harness public and parliamentary support for greater recognition.

The 550,000 Indigenous Australians make up 2.7% of the population.

They suffer disproportionately high rates of unemployment, imprisonment, drug abuse, alcoholism and disease.

'Change needed'

Ms Gillard, of the centre-left Labor party, said that practical efforts to help Australia's Aborigines and Torres Strait Islanders could not succeed without greater respect.

"The Australian constitution is the foundation document of our system of government, but it fails to recognise the special place of our first Australians," she said in a joint statement with the minister for indigenous affairs and the attorney-general.

"Constitutional recognition of Indigenous Australians is an important step towards building a nation based on strong relationships and mutual respect," she added.

"Recognition will demonstrate that we are a country that is united in acknowledging the unique and special place of our first peoples."

The referendum will ask the country to give constitutional recognition to indigenous people. It is unclear when the vote will take place.

Aboriginal leaders say a positive result would have a "dramatic effect" on the community's self-esteem.

Forty-four referendums have been held in Australia since 1901. Only eight have been passed.

_________________________________________________________________________________________________________________________________________________

play games for cash

unibet

**nirvana**- Posts : 18

Join date : 2010-08-19

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