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the graph of a parabola can show whether a quadratic equation has real solutions. put the following descriptions in order, from indicating two real solutions to indicating no real solutions
a parabola that touches the x-axis at a single point
a parabola that does not intersect the x-axis at all
a parabola that crosses the x-axis twice
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GPT-5 mini
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1. a parabola that crosses the x-axis twice (two real solutions; discriminant > 0)
2. a parabola that touches the x-axis at a single point (one real/repeated solution; discriminant = 0)
3. a parabola that does not intersect the x-axis at all (no real solutions; discriminant < 0)
2. a parabola that touches the x-axis at a single point (one real/repeated solution; discriminant = 0)
3. a parabola that does not intersect the x-axis at all (no real solutions; discriminant < 0)
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