Quadratic Functions — Test

Question 22 • Mathematics I

Which is the graph of f of x is equal to x squared minus 2 x plus 3 ?

Answer

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 2 comma 3), has a vertex at (negative 1 comma 2), and goes through (0 comma 3).

Image with description On a coordinate plane, a parabola opens up. It goes through (0 comma 3), has a vertex at (1 comma 2), and goes through (2 comma 3).

Image with description On a coordinate plane, a parabola opens up. It goes through (0 comma 3), has a vertex at (2 comma negative 1), and goes through (4 comma 3).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 4 comma 3), has a vertex at (negative 2 comma negative 1), and goes through (0 comma 3).

Explanation

Complete the square: x² − 2x + 3 = (x − 1)² + 2. So the parabola opens upward and has its vertex at (1, 2). Substituting x = 0 and x = 2 gives y = 3 at both points, matching the graph in choice D.

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