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find vertex find yintercept and x intercept
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There are two functions here: x^2-2x and x^2-2x-80. These can be rewritten: (x-1)^2-1 and (x-1)^2-81. They both have the same axis of symmetry which is the line x=1 on which the vertex sits for both, respectively (1,-1) and (1,-81). The y intercepts are respectively y=0 and -80 (when x=0). The x intercepts are respectively 0 and 2, and -8 and 10 and the curves have exactly the same U shape but the first sits apart from the second, so that the vertices are 80 apart. The x intercepts for the first curve are close together (2 apart), while those for the second curve are further apart (18), demonstrating how the arms of the U spread out as the curve moves away from the vertex. The two curves never intersect.

In case you're wondering how the x intercepts were calculated, at f(x) (i.e., y) = 0, (x-1)^2=1 or 81, and x-1=+1 or +9, so x=0 and 2, or -8 and 10.

by Top Rated User (1.2m points)

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