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We started with this:

y = 3x^2 - 1

Let me ask you... 
What is the
y value of points that live on the x-axis?

all points on the x-axis have a y value of 0 ... examples: ( -3 , 0 ) , ( -3/2 , 0 ) , ( 0 , 0 ) , ( 2, 0 )

All the y guys are 0 !

So, y = 0 !

y = 3x^2 - 1 ... 0 = 3x^2 - 1 ... solve this! add 1 to both sides, which gives 3x^2 = 1 which gives x^2 = 1/3 ... take the square root of both sides, which gives x = +/- 1 / sqrt( 3 )

x = -1 / sqrt( 3 ) or x = 1 / sqrt( 3 ) ... ( x is approximately equal to -.58 or .58 )

Hey -- these look great with our graph!

graph of y = 3x^2 - 1 ... the x-intercepts are x = -1 / sqrt( 3 ) and x = 1 / sqrt( 3 )