Graph linear and quadratic functions and identify intercepts, maxima, and minima.
Choose a graph window that shows the important features of a linear or quadratic function
Problem
For \(y=(x-10)^{2}-25\), a graph window must cover roots \(5\) and \(15\), the axis \(x=10\), the vertex \((10,-25)\), and the \(x\)-axis while keeping those features readable. Which graph window meets every criterion?
A useful graph window is not simply the largest one; it has to reveal the important geometry without flattening it into an unreadable picture. We’ll derive every landmark the window must contain, reject any bounds that clip one, and then judge the remaining scale by its margin and readability.
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