SOLUTION: Show me how to graph y=x^2+5x+3

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Question 116779: Show me how to graph y=x^2+5x+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To graph y=x%5E2%2B5x%2B3 simply plot a sequence of points and connect them. In other words, find y values for some given x values and plot the points (x,y).



So let's start at x=-6

Let's evaluate f%28-6%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-6%29=%28-6%29%5E2%2B5%28-6%29%2B3 Plug in x=-6. In other words, replace each x with -6.


f%28-6%29=%2836%29%2B5%28-6%29%2B3 Evaluate %28-6%29%5E2 to get 36.


f%28-6%29=%2836%29%2B-30%2B3 Multiply 5 and -6 to get -30


f%28-6%29=9 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-5%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-5%29=%28-5%29%5E2%2B5%28-5%29%2B3 Plug in x=-5. In other words, replace each x with -5.


f%28-5%29=%2825%29%2B5%28-5%29%2B3 Evaluate %28-5%29%5E2 to get 25.


f%28-5%29=%2825%29%2B-25%2B3 Multiply 5 and -5 to get -25


f%28-5%29=3 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-4%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-4%29=%28-4%29%5E2%2B5%28-4%29%2B3 Plug in x=-4. In other words, replace each x with -4.


f%28-4%29=%2816%29%2B5%28-4%29%2B3 Evaluate %28-4%29%5E2 to get 16.


f%28-4%29=%2816%29%2B-20%2B3 Multiply 5 and -4 to get -20


f%28-4%29=-1 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-3%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-3%29=%28-3%29%5E2%2B5%28-3%29%2B3 Plug in x=-3. In other words, replace each x with -3.


f%28-3%29=%289%29%2B5%28-3%29%2B3 Evaluate %28-3%29%5E2 to get 9.


f%28-3%29=%289%29%2B-15%2B3 Multiply 5 and -3 to get -15


f%28-3%29=-3 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-2%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-2%29=%28-2%29%5E2%2B5%28-2%29%2B3 Plug in x=-2. In other words, replace each x with -2.


f%28-2%29=%284%29%2B5%28-2%29%2B3 Evaluate %28-2%29%5E2 to get 4.


f%28-2%29=%284%29%2B-10%2B3 Multiply 5 and -2 to get -10


f%28-2%29=-3 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-1%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%28-1%29=%28-1%29%5E2%2B5%28-1%29%2B3 Plug in x=-1. In other words, replace each x with -1.


f%28-1%29=%281%29%2B5%28-1%29%2B3 Evaluate %28-1%29%5E2 to get 1.


f%28-1%29=%281%29%2B-5%2B3 Multiply 5 and -1 to get -5


f%28-1%29=-1 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%280%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%280%29=%280%29%5E2%2B5%280%29%2B3 Plug in x=0. In other words, replace each x with 0.


f%280%29=%280%29%2B5%280%29%2B3 Evaluate %280%29%5E2 to get 0.


f%280%29=%280%29%2B0%2B3 Multiply 5 and 0 to get 0


f%280%29=3 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%281%29


f%28x%29=x%5E2%2B5x%2B3 Start with the given function.


f%281%29=%281%29%5E2%2B5%281%29%2B3 Plug in x=1. In other words, replace each x with 1.


f%281%29=%281%29%2B5%281%29%2B3 Evaluate %281%29%5E2 to get 1.


f%281%29=%281%29%2B5%2B3 Multiply 5 and 1 to get 5


f%281%29=9 Now combine like terms


Now lets make a table of the values we have calculated 



 xy



 -69
 

 -53
 

 -4-1
 

 -3-3
 

 -2-3
 

 -1-1
 

 03
 

 19
Now plot the points



Now connect the points to graph y=x%5E2%2B5x%2B3 (note: the more points you plot, the easier it is to draw the graph)