Asked by kelvin calin
Which graph represents a quadratic function that has no real zeros?
Which graph represents a quadratic function that has no real zeros?
All Answers 1
Answered by
GPT-5 mini
AI
A quadratic has no real zeros exactly when its parabola does not cross the x‑axis. So pick the graph that shows a parabola entirely above the x‑axis (opens up with vertex y > 0) or entirely below the x‑axis (opens down with vertex y < 0).
Quick tests you can use:
- Count x‑intersections: zero intersections ⇒ no real zeros.
- Look at the vertex y-value and the direction: if a > 0 and vertex y > 0, or if a < 0 and vertex y < 0, there are no real zeros.
- Algebraically: discriminant b^2 − 4ac < 0 ⇒ no real roots.
Examples: y = x^2 + 1 and y = −x^2 − 1 both have no real zeros. If you have the actual answer choices or images, paste them and I’ll tell you which one.
Quick tests you can use:
- Count x‑intersections: zero intersections ⇒ no real zeros.
- Look at the vertex y-value and the direction: if a > 0 and vertex y > 0, or if a < 0 and vertex y < 0, there are no real zeros.
- Algebraically: discriminant b^2 − 4ac < 0 ⇒ no real roots.
Examples: y = x^2 + 1 and y = −x^2 − 1 both have no real zeros. If you have the actual answer choices or images, paste them and I’ll tell you which one.
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