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Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

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What is the range of \(a\) such that the roots of \(2x^2+ax+17=0\) are larger than \(-17?\)

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Consider a parabola \(y=3x^2-5x+2\) and a line that passes through \((-2,0)\) on the coordinate plane. If the parabola and line intersect at exactly two distinct points, what is the possible range for the slope \(m\) of the line?

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Find the vertex of the parabola \(y=4x^2+5x+5.\)

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