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Transformation of the graph of a quadratic function

Question:

Right-shit the graph of the quadratic function y = -x2 - 2x, n (n > 0) units to get the graph of y = -x2 + 4x - 3, what is the value of n?

Solution:

Use the completing square to find the vertex of y = -x2 - 2x

y = -x2 - 2x = -(x2 + 2x) = -(x2 + 2x + 1 - 1) = -(x2 + 2x + 1) + 1 = -(x + 1)2 + 1

Therefore, its vertex is (-1, 1) and axis of symmetry is x = -1, the graph is open downward. Because the coefficient of the x square term is negative.

Use the completing square to find the vertex of y = -x2 +4x - 3

y = -x2 +4x - 3 = -(x2 - 4x) - 3 = -(x2 - 4x + 4 - 4) - 3 = -(x2 - 4x + 4) + 4 - 3 = -(x - 2)2 + 1

Therefore, its vertex is (2, 1) and axis of symmetry is x = 2, the graph is open downward. Because the coefficient of the x square term is negative.

so n = 2 - (-1) = 2 + 1 = 3

Therefore, right shif the graph of y = -x2 - 2x, 3 units to get the graph of y = -x2 + 4x - 3