Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Sketch a quadratic from key features
Problem
Derive the quadratic with vertex \((2,~-1)\), opening up, and \(y\)-intercept \((0,~3)\), and graph it on the grid. State the equation, axis of symmetry, a symmetric point pair, zeros, and range.
Given features determine a quadratic only after the scale factor is fixed. We’ll begin with vertex form, use the stated opening for the coefficient’s sign, and substitute the supplied intercept to solve for its magnitude. The resulting rule then generates the symmetry axis, a reflected point, the zeros, and the range, giving several independent checks on the final sketch.
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