SOLUTION: I need help with this one please. Graph the quadratic function f(x)= 4(x+5)^2-1 Complete all of the steps required to find the information needed to be able to graph the functio

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I need help with this one please. Graph the quadratic function f(x)= 4(x+5)^2-1 Complete all of the steps required to find the information needed to be able to graph the functio      Log On


   

Question 332279: I need help with this one please.
Graph the quadratic function
f(x)= 4(x+5)^2-1
Complete all of the steps required to find the information needed to be able to graph the function by hand.
Thank-you ahead of time. I sincerely appreciate your time.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=4%28x%2B5%29%5E2-1, we need to plot a few points.


To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.


Let's find the y value when x=-7


y=4%28x%2B5%29%5E2-1 Start with the given equation.


y=4%28-7%2B5%29%5E2-1 Plug in x=-7.


y=4%28-2%29%5E2-1 Add -7 to 5 to get -2.


y=4%284%29-1 Square -2 to get 4.


y=16-1 Multiply 4 and 4 to get 16 .


y=15 Subtract 1 from 16 to get 15 .


So if x=-7, then y=15 which gives us the point (-7,15).


----------------------------


Let's find the y value when x=-6


y=4%28x%2B5%29%5E2-1 Start with the given equation.


y=4%28-6%2B5%29%5E2-1 Plug in x=-6.


y=4%28-1%29%5E2-1 Add -6 to 5 to get -1.


y=4%281%29-1 Square -1 to get 1.


y=4-1 Multiply 4 and 1 to get 4 .


y=3 Subtract 1 from 4 to get 3 .


So if x=-6, then y=3 which gives us the point (-6,3).


----------------------------


Let's find the y value when x=-5


y=4%28x%2B5%29%5E2-1 Start with the given equation.


y=4%28-5%2B5%29%5E2-1 Plug in x=-5.


y=4%280%29%5E2-1 Add -5 to 5 to get 0.


y=4%280%29-1 Square 0 to get 0.


y=0-1 Multiply 4 and 0 to get 0 .


y=-1 Subtract 1 from 0 to get -1 .


So if x=-5, then y=-1 which gives us the point (-5,-1).


----------------------------


Let's find the y value when x=-4


y=4%28x%2B5%29%5E2-1 Start with the given equation.


y=4%28-4%2B5%29%5E2-1 Plug in x=-4.


y=4%281%29%5E2-1 Add -4 to 5 to get 1.


y=4%281%29-1 Square 1 to get 1.


y=4-1 Multiply 4 and 1 to get 4 .


y=3 Subtract 1 from 4 to get 3 .


So if x=-4, then y=3 which gives us the point (-4,3).


----------------------------


Let's find the y value when x=-3


y=4%28x%2B5%29%5E2-1 Start with the given equation.


y=4%28-3%2B5%29%5E2-1 Plug in x=-3.


y=4%282%29%5E2-1 Add -3 to 5 to get 2.


y=4%284%29-1 Square 2 to get 4.


y=16-1 Multiply 4 and 4 to get 16 .


y=15 Subtract 1 from 16 to get 15 .


So if x=-3, then y=15 which gives us the point (-3,15).


----------------------------


Now let's make a table of the values we just found.


Table of Values:





xy
-715


-63


-5-1


-43


-315

Now let's plot the points:




Graph:


Now draw a curve through all of the points to graph y=4%28x%2B5%29%5E2-1:


Graph of y=4%28x%2B5%29%5E2-1