Practice Test

Question 3 • Algebra: Concepts and Connections

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

Answer

Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled y. The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An upward-opening U-shaped parabola has its vertex at negative 2 comma negative 1. On the left, the curve passes through negative 3 comma 0 and negative 4 comma 3. On the right, the curve passes through negative 1 comma 0 and 0 comma 3. Both ends extend upward to the top edge of the grid near 5.

Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled y. The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An upward-opening U-shaped parabola has its vertex at 1 comma 2. The curve passes through 0 comma 3 and 2 comma 3, with both ends extending upward to the top edge of the grid near 5.

Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled y. The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An upward-opening U-shaped parabola has its vertex at negative 1 comma 2. The curve passes through negative 2 comma 3 and 0 comma 3, with both ends extending upward to the top edge of the grid near 5.

Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled y. The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An upward-opening U-shaped parabola has its vertex at 2 comma negative 1. On the left, the curve passes through 1 comma 0 and 0 comma 3. On the right, the curve passes through 3 comma 0 and 4 comma 3. Both ends extend upward to the top edge of the grid near 5.

Explanation

Complete the square: x² + 2x + 3 = (x + 1)² + 2. The graph is an upward-opening parabola with vertex at (−1, 2). It also passes through (−2, 3) and (0, 3), so choice C matches.

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