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Making the Connection Between Graphing and Solving

One more:

Graphy = x^2 - x - 2, label five points and find the zeros:

 

1Complete the square:

y = x^2 - x - 2 gives y = ( x^2 - x ___ ) - 2 ___ which gives y = ( x^2 - x + 1/4 ) - 2 - 1/4 which gives y = ( x - 1/2 )^2 - 9/4

2Graph it.  (I've got it below, but go ahead and try it yourself!)

 

3Find the zeros:

x^2 - x - 2 = 0 gives ( x - 2 ) ( x + 1 ) = 0 which gives x - 2 = 0 or x + 1 = 0 which gives x = 2 or x = -1

Duuuude...  These look great with our graph:

graph of y = x^2 - x - 2 ... the x-intercepts are x = -1 and x = 2

YOUR TURN:

Graphy = x^2 - 4, label the usual five points and find the zeros:

 

Graphy = 3x^2 - 12x + 11, label the usual three points and
find the zeros: