Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Write a quadratic function from a vertex and one other graph feature
Problem
Use the feature plot to build a quadratic with vertex \((2,3)\) that opens upward and passes through \((3,5)\). Start with \(f(x)=a(x-2)^{2}+3\), substitute the second point to solve \(a\), state the function, and verify both the opening direction and point.
A known vertex fixes the horizontal and vertical shifts in vertex form, leaving only the vertical scale unknown. We’ll substitute the second plotted point, solve for that scale after squaring its horizontal displacement, and verify the completed rule against the vertex, the point, and the required opening direction.
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