Geometry

Conic Sections

Conics - Parabola - General

         

If the two parabolas y=2x23x+6y=2x^2-3x+6 and y=2x2ax+1y=-2x^2-ax+1 meet at a single point, what is the product of all possible values for a?a?

What is the range of aa such that the roots of 2x2+ax+17=02x^2+ax+17=0 are larger than 17?-17?

Consider a parabola y=3x25x+2y=3x^2-5x+2 and a line that passes through (2,0)(-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 mm of the line?

Find the vertex of the parabola y=4x2+5x+5.y=4x^2+5x+5.

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

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