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Easy: Shifts of y = x²
Moving y = x² right h and up k gives y = (x − h)² + k. With a vertex and another point, write y = a(x − h)² + k, substitute the point, and solve for a.
Write the equation of each parabola in vertex form.
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Substitute the vertex for h and k and the point for x and y, then solve for a. Vertex (2, 1) and point (4, 9): 9 = a(4 − 2)² + 1, so a = 2.
The new graph reaches each height 3 units later, so to get the old value you must subtract 3 from x first. Right is minus, left is plus.
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