Advanced MathMediumParabola and a line below it
Advanced Math practice question
The parabola y = x² and the horizontal line y = −1 are graphed in the xy-plane. At how many points do the two graphs intersect?
- A. 0Correct
- B. 1
- C. 2
- D. Infinitely many
Answer: A. 0
An intersection would need x² = −1, but a square is never negative. The parabola never dips below the x-axis, so it never reaches y = −1: no intersections.
Why the other answers are wrong
- B. 1
- One intersection happens when the line touches the vertex, which is y = 0, not y = −1.
- C. 2
- Two intersections happen for lines ABOVE the vertex, such as y = 1 (at x = ±1).
- D. Infinitely many
- The graphs are different curves; they can't share infinitely many points.
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