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Parabolas quiz

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  • What is the standard form equation for a vertical parabola?
    The standard form is y = a(x-h)² + k.
  • How does the sign of 'a' affect the direction a vertical parabola opens?
    If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.
  • Where is the vertex located in the equation y = a(x-h)² + k?
    The vertex is at the point (h, k).
  • What is the axis of symmetry for a vertical parabola?
    The axis of symmetry is x = h.
  • What is the standard form equation for a horizontal parabola?
    The standard form is x = a(y-k)² + h.
  • How does the sign of 'a' affect the direction a horizontal parabola opens?
    If 'a' is positive, the parabola opens to the right; if 'a' is negative, it opens to the left.
  • Where is the vertex located in the equation x = a(y-k)² + h?
    The vertex is at the point (h, k).
  • What is the axis of symmetry for a horizontal parabola?
    The axis of symmetry is y = k.
  • What is a parabola in terms of conic sections?
    A parabola is a conic section defined as all points equidistant from a fixed line (directrix) and a fixed point (focus).
  • Where is the directrix located relative to the parabola?
    The directrix is always outside the parabola.
  • Where is the focus located relative to the parabola?
    The focus is always inside the parabola, in the direction it opens.
  • How do you switch from a vertical to a horizontal parabola equation?
    Switch the roles of x and y, and also switch h and k in the equation.
  • What does the axis of symmetry represent in a parabola?
    It is a line that divides the parabola into two mirror-image halves.
  • What is the relationship between any point on a parabola, the directrix, and the focus?
    Any point on the parabola is the same distance from the directrix as it is from the focus.
  • Why is it important to recognize the vocabulary of directrix and focus?
    Understanding these terms helps identify and describe parabolas as conic sections.