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For a quadratic polynomial $ax^2+bx+c$ with $a\neq 0$, which statement is always true about the graph of $y=ax^2+bx+c$?
AIt always cuts the $x$-axis at exactly two points
BIt can cut the $x$-axis at at most two points
CIt never touches the $x$-axis
DIt always has exactly one zero
Answer & Solution
Correct answer: B. It can cut the $x$-axis at at most two points
A quadratic graph is a parabola. It may intersect the $x$-axis at two distinct points, touch it at one point, or not meet it at all. Therefore, it can cut the $x$-axis at at most two points.
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