Advanced MathMediumIdentifying a quadratic with no x-intercepts
Advanced Math practice question
Which of the following equations has a graph in the xy-plane with no x-intercepts?
- A. y = x² + 1Correct
- B. y = x² − 1
- C. y = (x − 1)²
- D. y = 1 − x²
Answer: A. y = x² + 1
x² + 1 is at least 1 for every x, so the graph never reaches the x-axis. The others all equal 0 for some x.
Why the other answers are wrong
- B. y = x² − 1
- x² − 1 = 0 at x = ±1.
- C. y = (x − 1)²
- (x − 1)² = 0 at x = 1.
- D. y = 1 − x²
- 1 − x² = 0 at x = ±1.
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