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Question 3 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

Which is the graph of the function f of x is equal to 1 half x squared plus 2 x minus 6 ?

Answer

Image with description A coordinate plane with a parabola. The x and y axes are labeled form negative 10 to 10 in increments of 2. The parabola opens upward, passes through approximately the point negative 8 comma 10, has a vertex at approximately negative 2 comma negative 8, crosses the y-axis at the point 0 comma negative 6, and passes through approximately the point 4 comma 10.

Image with description A coordinate plane with a parabola. The x and y axes are labeled from negative 10 to 10 in increments of 2. The parabola opens upward, crosses the x-axis at two points, and has a vertex below the x-axis.

Image with description A coordinate plane with a parabola. The x and y axes are labeled form negative 10 to 10 in increments of 2. The parabola opens upward, passes through the point negative 6 comma 0, has a vertex at negative 2 comma negative 8, and passes through the point 2 comma 0.

Image with description A coordinate plane with a parabola. The x and y axes are labeled form negative 10 to 10 in increments of 2. The parabola opens upward, passes through the point negative 8, comma negative 6, has a vertex at negative 4, comma negative 10, and passes through the point 4, comma 6.

Explanation

The coefficient of x² is positive, so the parabola opens upward. Its vertex is at x = −2, and f(−2) = −8, giving the vertex (−2, −8). Solving f(x) = 0 gives x = −6 and x = 2, so the graph crosses the x-axis at (−6, 0) and (2, 0). These features match choice A.

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