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.
More Advanced Math questions
- Medium
What are the solutions to x² − 5x + 6 = 0? - Medium
The graph of f(x) = (x − 3)² + 4 is a parabola. What are the coordinates of its vertex? - Medium
If x² − 2x − 8 = (x + 2)(x − a), what is the value of a? - Medium
If √(x + 5) = 4, what is the value of x? - Medium
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))? - Medium
What are the solutions to x² + 6x + 8 = 0?
Not affiliated with the College Board. SAT is a trademark of the College Board.