SOLUTION: 1. Solve. (x + 4)^2 = 7 2. Find the constant term that should be added to make the following expression a perfect-square trinomial. x^2 + 7x 3.Graph the following equation:

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1. Solve. (x + 4)^2 = 7 2. Find the constant term that should be added to make the following expression a perfect-square trinomial. x^2 + 7x 3.Graph the following equation:       Log On


   

Question 110812: 1. Solve. (x + 4)^2 = 7
2. Find the constant term that should be added to make the following expression a perfect-square trinomial.
x^2 + 7x
3.Graph the following equation:
y = –x^2 + 6x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1



Start with the given equation



Take the square root of both sides



Subtract 4 from both sides to isolate x.



-----------------------------------
Answer:

So our solution is:



This means our solution breaks down to:



or





#2



x%5E2%2B7x Start with the given equation

Take half of the x coefficient 7 to get 3.5 (ie 7%2F2=3.5)
Now square 3.5 to get 12.25 (ie %283.5%29%5E2=12.25)



x%5E2%2B7x%2B12.25 Add this result (12.25) to the expression. Now the expression x%5E2%2B7x%2B12.25 is a perfect square trinomial.



#3


In order to graph y=-x%5E2%2B6x, we need to plot some points.

We can start at any x value, so lets start at x=1




Lets evaluate f%281%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%281%29=-%281%29%5E2%2B6%281%29 Plug in x=1


f%281%29=-1%2B6%281%29 Evaluate %281%29%5E2 to get 1

f%281%29=-1%2B6 Multiply 6 and 1 to get 6

f%281%29=5 Now combine like terms


So when x=1, f%28x%29=5



-------Now lets find another point-------



Lets evaluate f%282%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%282%29=-%282%29%5E2%2B6%282%29 Plug in x=2


f%282%29=-4%2B6%282%29 Evaluate -1%282%29%5E2 to get -14

f%282%29=-4%2B12 Multiply 6 and 2 to get 12

f%282%29=8 Now combine like terms


So when x=2, f%28x%29=8



-------Now lets find another point-------



Lets evaluate f%283%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%283%29=-%283%29%5E2%2B6%283%29 Plug in x=3


f%283%29=-9%2B6%283%29 Evaluate -1%283%29%5E2 to get -19

f%283%29=-9%2B18 Multiply 6 and 3 to get 18

f%283%29=9 Now combine like terms


So when x=3, f%28x%29=9



-------Now lets find another point-------



Lets evaluate f%284%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%284%29=-%284%29%5E2%2B6%284%29 Plug in x=4


f%284%29=-16%2B6%284%29 Evaluate -1%284%29%5E2 to get -116

f%284%29=-16%2B24 Multiply 6 and 4 to get 24

f%284%29=8 Now combine like terms


So when x=4, f%28x%29=8



-------Now lets find another point-------



Lets evaluate f%285%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%285%29=-%285%29%5E2%2B6%285%29 Plug in x=5


f%285%29=-25%2B6%285%29 Evaluate -1%285%29%5E2 to get -125

f%285%29=-25%2B30 Multiply 6 and 5 to get 30

f%285%29=5 Now combine like terms


So when x=5, f%28x%29=5


Now lets make a table of the values we have calculated 



 xy



 15
 

 28
 

 39
 

 48
 

 55
Now plot the points



Now connect the points to graph y=-x%5E2%2B6x (note: the more points you plot, the easier it is to draw the graph)