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Notes For Parabolas

  • (intro) A path of a projectile is known to have the shape of a _______________.

  • (page 1) In the general form of the conics equation, Ax2 + By2 + Cx + Dy + F = 0, the value of A or B must be ________ to obtain a parabola.

  • (page 2) The standard equation for a parabola which opens upward or downward is given by: ______________________________ where (h, k) is the vertex and a contains important information about the shape of the parabola.

  • (page 3) Increasing the value of k in the standard equation results in moving the parabola ______________.

  • (page 3) Decreasing the value of h in the standard equation results in moving the parabola to the __________.

  • (page 3) Increasing the value of a in the standard equation results in making the parabola ___________________.

  • (page 3) If the equation is of the form y - k = a(x - h)2 and a is ________________, then the parabola opens downward.

  • (page 6) If the equation is of the form x - h = a(y - k)2 and a is ________________, then the parabola opens to the right.

  • (page 10) A double-napped cone is cut by a plane that is __________________ to the generator to produce a parabola.