Question #be5ca

1 Answer
Dec 4, 2017

The first one should look like this: graph{-2(x+2)^2+6 [-10, 10, -5, 5]}
The second one should look like this: graph{1/2(x)^2-6x+13 [-10, 10, -5, 5]}

Explanation:

Our method for graph the parabola will be like this:
We find the values of a, h, and k.
Then, we graph the other four points by doing the following:
We will do h-2a, h-a, h+a, and h+2a for the x values and plug them in the equation to find the y values.
The minimum/maximum point of a parabola is (h,k)

#-2(x+2)^2+6#:

This equation is in the form #a(x-h)^2+k#

Therefore,
#a=-2#
#h=-2#
#k=6#

The x values are:
#-2-2(-2)=2#
#-2-(-2)=0#
#-2#
#-2+(-2)=-4#
#-2+2(-2)=-6#

Plug in the values in the equation to get the following y values.
#-2-2(-2)=2# =>-28
#-2-(-2)=0# =>-2
#-2# =>6
#-2+(-2)=-4# =>-2
#-2+2(-2)=-6# =>-28

Plot the points an you have the answer!

#1/2(x)^2-6x+13#:

This equation is in the form #ax^2+bx+c#
We have to know that #h=(-b)/(2a)#
Plug in this value to the equation to get k.
Therefore,
#a=1/2#
#h=6#
#k=-5#

The x values are:
#6-2(1/2)=5#
#6-1/2=5 1/2#
#6#
#6+1/2=-6 1/2#
#6+2(1/2)=7#

Plug in the values in the equation to get the following y values.
#6-2(1/2)=5# =>-4.5
#6-1/2=5 1/2# =>-4.875
#6# =>-5
#6+1/2=-6 1/2#=>-4.875
#6+2(1/2)=7#=>-4.5

Plot the points an you have the answer!