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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.
  • Where is the vertex located in the equation y = a(x−h)² + k?
    The vertex is at the point (h, k).
  • How does the value of 'a' affect the direction a vertical parabola opens?
    If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.
  • What is the axis of symmetry for a vertical parabola in standard form?
    The axis of symmetry is the vertical line x = h.
  • How do you write the equation for a horizontal parabola?
    The equation is x = a(y−k)² + h.
  • For a horizontal parabola, what does a positive 'a' indicate?
    A positive 'a' means the parabola opens to the right.
  • What does a negative 'a' mean for a horizontal parabola?
    A negative 'a' means the parabola opens to the left.
  • Where is the vertex of a horizontal parabola 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 the horizontal line y = k.
  • What is a parabola in terms of distance from a point and a line?
    A parabola is the set of all points equidistant from a fixed point (focus) and a fixed line (directrix).
  • Where is the directrix located relative to the parabola?
    The directrix is always outside the parabola.
  • Where is the focus located in relation to the parabola?
    The focus is always inside the parabola, on the side it opens toward.
  • How do you determine the direction a parabola opens from its equation?
    Check the sign of 'a'; positive opens up/right, negative opens down/left depending on orientation.
  • What happens to the equation of a parabola when switching from vertical to horizontal orientation?
    You switch the roles of x and y, and also h and k in the equation.
  • Why is it important to recognize the focus and directrix in parabolas?
    They help define the parabola as a conic section and explain its geometric properties.