Practice Exam

Question 29 • Algebra I

Which is the graph of a quadratic equation that has a negative discriminant?

Answer

Image with description On a coordinate plane, the x and y axes are ranges from negative 10 to 10 with an increment of 2. The curve represent the parabola which is opening downward. The vertex of parabola is located at negative 2 comma 8. The curve passes through the point negative 4 comma 4, 0 comma 4, negative 5 comma 0 and 1 comma 0. The arrow is present on both ends of the curve.

Image with description On a coordinate plane, the x and y axes are ranges from negative 10 to 10 with an increment of 2. The curve represent the parabola which is opening upward. The vertex of parabola is located at negative 2 comma 4. The curve passes through the point negative 4 comma 8 and 0 comma 8. The arrow is present on both ends of the curve.

Image with description On a coordinate plane, the x and y axes are ranges from negative 10 to 10 with an increment of 2. The curve represent the parabola which is opening upward. The vertex of parabola is located at negative 2 comma 0. The curve passes through the point negative 4 comma 4, 0 comma 4, negative 5 comma 8 and 1 comma 8. The arrow is present on both ends of the curve.

Image with description On a coordinate plane, the x and y axes are ranges from negative 10 to 10 with an increment of 2. The curve represent the parabola which is opening downward. The vertex of parabola is located at negative 2 comma 0. The curve passes through the point negative 4 comma negative 4, 0 comma negative 4, negative 5 comma negative 8 and 1 comma negative 8. The arrow is present on both ends of the curve.

Explanation

A quadratic has a negative discriminant when it has no real x-intercepts, so its graph does not cross or touch the x-axis. In choice B, the parabola opens upward and its vertex is at (−2, 4), above the x-axis, so the entire graph stays above it. Choices C and D touch the x-axis at their vertices, and A crosses it twice.

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