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Parabolas quiz

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  • How is a parabola formed in conic sections?
    A parabola is formed by slicing a three-dimensional cone with a heavily tilted two-dimensional plane.
  • What are the focus and directrix of a parabola?
    The focus is a point and the directrix is a line, both equidistant from the vertex of the parabola.
  • Where is the focus located for an upward-opening parabola?
    For an upward-opening parabola, the focus is above the vertex.
  • How do you determine the direction a parabola opens using the p value?
    A positive p value means the parabola opens up (or right for horizontal), while a negative p value means it opens down (or left for horizontal).
  • What is the standard form equation for a vertical parabola with vertex at the origin?
    The standard form is y = (1/(4p))x² for a vertical parabola with vertex at the origin.
  • How do you find the p value from the standard form equation of a parabola?
    Set the coefficient of the linear term equal to 4p and solve for p by dividing by 4.
  • What is the directrix for a vertical parabola that opens upward?
    The directrix is a horizontal line located p units below the vertex.
  • How do you find the vertex of a parabola in standard form?
    The vertex is at (h, k), where h and k are the values that shift the parabola horizontally and vertically.
  • What changes in the equation when dealing with a horizontal parabola?
    For a horizontal parabola, the x and y variables are switched in the equation.
  • How do you determine the direction a horizontal parabola opens?
    A positive p value means the parabola opens to the right, and a negative p value means it opens to the left.
  • What is the directrix for a horizontal parabola?
    The directrix is a vertical line located p units to the left (if opening right) or right (if opening left) of the vertex.
  • How do you find the focus of a parabola given the vertex and p value?
    Move p units from the vertex in the direction the parabola opens to locate the focus.
  • How do you determine the width of a parabola when graphing?
    From the focus, move 2|p| units perpendicular to the axis of symmetry to find the width points.
  • What is the axis of symmetry for a vertical and a horizontal parabola?
    The axis of symmetry is vertical for vertical parabolas and horizontal for horizontal parabolas.
  • What is the final step in graphing a parabola after finding the vertex, focus, and width points?
    Connect the points with a smooth curve to form the parabola, then draw the directrix.