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Question 5 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

The graph of which function has an axis of symmetry at x is equal to 3 ?

Answer

f of x is equal to x squared minus 3 x minus 3 Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A parabola opens upward with its vertex at approximately the point 2 comma negative 6, with the left side rising to approximately the point negative 2 comma 4 with an arrow and the right side rising to approximately the point 6 comma 4 with an arrow, indicating the parabola continues beyond the top of the plane in both directions.

f of x is equal to x squared plus 6 x plus 3 Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A parabola opens upward with its vertex at approximately the point negative 2 comma negative 6, with the left side rising to approximately the point negative 6 comma 4 with an arrow and the right side rising to approximately the point 2 comma 4 with an arrow, indicating the parabola continues beyond the top of the plane in both directions.

f of x is equal to x squared minus 6 x minus 1 Image with description A coordinate plane has both x and y axes labeled from negative 10 to 10. A curve is plotted that passes through the point 0 comma negative 1, and has a vertex at 3 comma negative 10, and increases to 6 coma 0.

f of x is equal to x squared plus 3 x plus 1 Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A parabola opens upward with its vertex at approximately the point negative 2 comma 0 on the x-axis, with both sides rising steeply, the left side extending to approximately the point negative 6 comma 10 with an arrow and the right side extending to approximately the point 2 comma 10 with an arrow, indicating the parabola continues beyond the top of the plane in both directions.

Explanation

For a quadratic function f(x) = ax² + bx + c, the axis of symmetry is x = −b/(2a). In choice A, a = 1 and b = −6, so the axis is x = −(−6)/(2·1) = 3. Its vertex is also described as being at x = 3, confirming that choice A is correct.

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