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A student claims: 'Since this parabola opens upward, it must have 2 real zeroes.'
Which single fact about the graph would PROVE the claim false?

Class 10Graphical Meaning of ZeroesAlgebra — Polynomials
  • AThe parabola lies entirely above the -axis
  • BThe parabola is symmetric about a vertical line
  • CThe vertex is the lowest point
  • DThe arms go upward on both sides

Step-by-Step Solution

An upward parabola can still miss the -axis. If it lies entirely above the -axis it has 0 real zeroes, disproving the claim.
Answer: A) The parabola lies entirely above the -axis

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