Algebra 1
Quadratic equations and functions
Transformations of quadratic functions
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Question 1
168123
The parent function is \(f(x) = x^2\). Describe the transformation that produces each function below and state the vertex of each.
(a) \(g(x) = x^2 + 5\)
(b) \(h(x) = x^2 - 3\)
(a) \(g(x) = x^2 + 5\): shifted 5 units up. Vertex: \((0, 5)\).
(b) \(h(x) = x^2 - 3\): shifted 3 units down. Vertex: \((0, -3)\).
In both cases the shape and width are unchanged — only the vertical position of the vertex changes.
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