Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Match quadratic forms to directly visible features
Problem
Analyze the equivalent forms \(x^{2}-6x+8\), \((x-2)(x-4)\), and \((x-3)^{2}-1\). From standard form read the \(y\text{-}\text{intercept}\) and leading coefficient, from factored form read the zeros, and from vertex form read the vertex, axis, and extremum; then state the shared opening direction.
Big Picture
What this problem is really about
One parabola can carry several algebraic descriptions, each acting like a different lens. We’ll verify the forms are equivalent, then read the vertical intercept and opening from standard form, the zeros from factored form, and the vertex, axis, and extremum from completed-square form.
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