Graph linear and quadratic functions and identify intercepts, maxima, and minima.
Find the x-intercepts, axis of symmetry, and vertex of a quadratic in factored form
Problem
Analyze \(y=(x-2)(x-6)\) from its factored form. Find \(\text{both}~\text{zeros}\), use their midpoint for the axis of symmetry, evaluate the function there for the vertex, and determine the opening direction and \(y\)-intercept. Identify the complete feature set supported by your work.
Big Picture
What this problem is really about
Factored form reveals where a quadratic reaches zero, and symmetry connects those crossings to the rest of the graph. We’ll extract the roots, average them to locate the axis, evaluate there for the vertex, and complete the picture with the leading sign and vertical-axis intercept.
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