Month: November 2018

This week in math we learned how to graph the reciprocal of a quadratic function. Below will be an example of how to do this:

the first step is to graph the parent function which would look like this. 

 

By looking at the graph you can determine a couple of things.

asymptotes: X= 1.7, x=-1.7 y=0

invariant point (1.6,1)(-1.6,1)(-1.8,-1)(1.8,1)

This gives you all the information that you need to graph the equation once you reciprocate it

the reciprocated function should look like this

the hyperbola above the x-axis is located at the reciprocal of the vertex which in this case is

The end result should look like this.

This week in math we learned how to determine the points of intersection of a linear absolute value equation, for example

:|2x-3|=9

the first is to split the equation into separate ones. one of them you have to replace the absolute value signs with brackets then place a negative in front that has to be distributed followed by solving as shown below.

-(2x-3)=9

-2x+3=9

-2x=6

x=-3

The second step is to just remove the absolute value signs from the equation then solve

2x-3=9

2x=12

x=6

you can now determine that for the two points of intersection x would equal x=-3 and x=6

 

 

 

this week in math we learned how to determine the points of intersection with a linear and quadratic system

the two systems that are going to be used are

and

First, you have to graph the quadratic which should not be that difficult since it is already in vertex form

the next step is to graph the linear system which involves a few more steps

first you must rearrange the system so that the Y is isolated and positive. After you rearrange the linear function it should look like this

from this, you can determine that the y-intercept is 3 and that it has a positive slope of 3. you now should have all the information to graph it.

from this point, you simply follow the course of both functions to find where they intersect with one another

in this case the there were two points that intersected, they were (1,6) and (-2.5,-4.5)

 

This week we learned how to solve a quadratic inequality.

example:

The first step would be to rearrange the inequality but in this case, it is not necessary.

so you would the factor the equation

 

The next step is to choose a number to use as a test point to determine which section of the graph satisfies the inequality

 

 

This is not true so it does not satisfy the inequality

Then test another point between -3 and 4, 0 will be the number that is used

 

this is true so it satisfies the inequality

lastly, you have to test a point that is greater than or equal to 4, we will use 5

 

this is not true therefore it does not satisfy the inequality. This means that the only solution is

 

 

 

 

This week in math we learned how to solve a word problem for quadratic functions. The following is an example:

A TV company sells TVs for $400. At that price, they can sell 500 per week, the company predicts that for every $50 increase in price, they will sell 20 fewer TVs. what price for a TV will maximize the revenue?

The first step is come up with figure out what formula to use based on the vocabulary used in this case you would use the formula to figure out revenue

Revenue=(price)(#of sales)

The next step is to foil this equation

Next, you have to get the function to vertex form by completing the square

Then factor and add

Vertex:(8.5,272,250)

Now you know that to maxamize revenue they can increase the price 8.5 times for and increase in profit of $72,250