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Conic Sections

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

Conics - Parabola - General

If the two parabolas $$y=2x^2-3x+6$$ and $$y=-2x^2-ax+1$$ meet at a single point, what is the product of all possible values for $$a?$$

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

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?

Find the vertex of the parabola $$y=4x^2+5x+5.$$

A parabola passes through the following three points: $(3,0), (9,0), (1,64).$ What is the vertex of the parabola?

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