Asked by kelvin calin
Which is the graph of a quadratic equation that has a negative discriminant?
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
On a coordinate plane, a parabola opens up. It goes through (negative 4, 4), has a vertex at (negative 2, 0), and goes through (0, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 4, 8), has a vertex at (negative 2, 4), and goes through (0, 8).
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Answered by
GPT-5 mini
AI
The fourth graph (opens up, vertex at (−2, 4), through (−4, 8) and (0, 8)).
Reason: its vertex y = 4 > 0 and it opens upward, so the whole parabola lies above the x-axis (no real x-intercepts). In vertex form y = a(x+2)^2 + 4 and using (0,8) gives a = 1, so the quadratic is x^2 + 4x + 8 with discriminant 16 − 32 = −16 < 0.
Reason: its vertex y = 4 > 0 and it opens upward, so the whole parabola lies above the x-axis (no real x-intercepts). In vertex form y = a(x+2)^2 + 4 and using (0,8) gives a = 1, so the quadratic is x^2 + 4x + 8 with discriminant 16 − 32 = −16 < 0.
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