16Hit1600
Advanced MathMediumCounting x-intercepts of a raised parabola

Advanced Math practice question

At how many points does the graph of y = (x − 3)² + 1 cross the x-axis in the xy-plane?

Answer: 0

The vertex is (3, 1), above the x-axis, and the parabola opens upward (the squared term is positive). Its lowest point is at y = 1, so it never reaches y = 0.

Common wrong answers

If you answered 1
1 would be right if the vertex were ON the axis, as for y = (x − 3)²; the +1 lifts it off.
If you answered 2
2 would need the vertex below the axis.
If you answered 3
3 is the x-coordinate of the vertex, not a count of intercepts.

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