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This one number can tell you whether the solutions to a quadratic equation are real or non-real, and whether they are distinct or repeated.

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\[f(x)=ax^2+bx+c\]

If \(b>10, 0<a<2, c=3\), how many times does the graph \(y=f(x)\) cross the x-axis?

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If the curve \(y=x^2+bx+c\) touches the \(x\)-axis at some point and intersects the y-axis at \((0,9)\), find the absolute value of \(b\).

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