Problem

Extract standard-form graph features for \(y=x^{2}-4x+3\).

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What this problem is really about

Standard form gives some graph features immediately, while others emerge from targeted calculations. We’ll use the leading and constant coefficients for opening and the vertical intercept, calculate the symmetry axis and vertex, factor for horizontal intercepts, and let the extremum determine the range.

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a=1>0 opens up; axis x=2; vertex y(2)=-1 so(2,-1); factorization=(x+1)(x+3); x-intercepts=(-1,0),(-3,0); y-intercept=(0,3); range=[-1,∞)

a=1>0 opens up; axis x=-b/a=4; vertex y(4)=3 so(4,3); factorization=(x−1)(x−3); x-intercepts=(1,0),(3,0); y-intercept=(0,3); range=[3,∞)

a=1>0 opens up; axis x=-b/(2a)=2; vertex y(2)=-1 so(2,-1); factorization=(x−1)(x−3); x-intercepts=(1,0),(3,0); y-intercept=(0,3); range=[-1,∞)

a=1>0 opens up; axis x=2; vertex y(2)=-1 so(2,-1); factorization=(x−1)(x−3); x-intercepts=(1,0),(3,0); y-intercept=(0,-4) from b; range=[-1,∞)

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Extract standard-form graph features for \(y=x^{2}-4x+3\).

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