Graph the function f(x)=3×2-3?

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Answer 1 · 2018-03-21T17:49:24

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Assuming you mean #f(x)=3x^2-3#

#f(x)# simply means a given function. So, therefore, we just plot the graph #3x^2-3#.

Set up a table of values, some negative and positive, for example when #x=-2,-1,0,1,2#

when #x=-2#
#f(x)=3(-2)^2-3=9#

when #x=-1#
#f(x)=3(-1)^2-3=0#

when #x=0#
#f(x)=3(0)^2-3=-3#

when #x=1#
#f(x)=3(1)^2-3=0#

when #x=2#
#f(x)=3(2)^2-3=9#

We, therefore, would plot these points on a graph and then join them up. See graph below:

graph{3x^2-3 [-5.986, 6.504, -3.195, 3.05]}

As you can see, the graph cuts the #y# axis at #(0,-3)#. You can find this by using #x=0#, getting that #y=-3#

#therefore# Turning point=#(0,-3)#

Finding the roots:

roots are where #y = 0 #

#=> 3x^2-3=0 #

#=> x^2-1= 0 #

#=> x^2 = 1 #

#=> x = -1,1 #

roots can be plotted on the graph as #(1,0)# and #(-1,0)#