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

Which is the graph of f of x is equal to open paren x minus 1 close paren times open paren x plus 4 close paren ?

Answer

Image with description A coordinate plane with downward-opening parabola. Both the axis are labeled from negative 6 to 6 with increments of 2. The curve represents a quadratic function with its maximum vertex located at the coordinate points 1 point 5 comma 6 point 2 5. Moving symmetrically outward from this vertex, the parabola crosses the vertical axis at a y-intercept of 0 comma 4 and intersects the horizontal axis at 2 x-intercepts located at negative 1 comma 0 and 4 comma 0. The two arms of the curve extend downward into the lower quadrants, passing perfectly through the grid line intersections at negative 2 comma negative 6 and 5 comma negative 6.

Image with description A coordinate plane with upward-opening parabola. Both the axis are labeled from negative 6 to 6 with increments of 2. The curve represents a quadratic function with its minimum vertex located at the coordinate points negative 1 point 5 comma negative 6 point 2 5. Moving symmetrically outward from this vertex, the parabola crosses the vertical axis at a y-intercept of 0 comma negative 4 and intersects the horizontal axis at two x-intercepts located at negative 4 comma 0 and 1 comma 0. The two arms of the curve extend upward into the upper quadrants, passing through the grid line intersections at negative 5 comma 6 and 2 comma 6.

Image with description A coordinate plane with downward-opening parabola. Both the axis are labeled from negative 6 to 6 with increments of 2. The curve represents a quadratic function with its maximum vertex located at the coordinate points negative 1 point 5 comma 6 point 2 5. Moving symmetrically outward from this vertex, the parabola crosses the vertical axis at a y-intercept of 0 comma 4 and intersects the horizontal axis at two x-intercepts located at negative 4 comma 0 and 1 comma 0. The two arms of the curve extend downward into the lower quadrants, passing through the grid line intersections at negative 5 comma negative 6 and 2 comma negative 6.

Image with description A coordinate plane with upward-opening parabola. Both the axis are labeled from negative 6 to 6 with increments of 2. The curve represents a quadratic function with its minimum vertex located at the coordinate points 1 point 5 comma negative 6 point 2 5. Moving symmetrically outward from this vertex, the parabola crosses the vertical axis at a y-intercept of 0 comma negative 4 and intersects the horizontal axis at two x-intercepts located at negative 1 comma 0 and 4 comma 0. The two arms of the curve extend upward into the upper quadrants, passing through the grid line intersections at negative 2 comma 6 and 5 comma 6.

Explanation

The factors give the zeros directly: x − 1 = 0 gives x = 1, and x + 4 = 0 gives x = −4. The leading coefficient is positive, so the parabola opens upward. Its y-intercept is f(0) = (−1)(4) = −4, matching the graph with x-intercepts −4 and 1 and y-intercept −4: choice B.

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