Geometry
Conic Sections
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?