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Parabolas quiz #1 Flashcards

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Parabolas quiz #1
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  • As the absolute value of the coefficient 'a' in a parabola's equation increases, how does the shape of the parabola change?
    As |a| increases, the parabola becomes narrower (steeper), meaning it opens more sharply.
  • What condition must be met for a parabola to have a minimum value at its vertex?
    A parabola will have a minimum value at its vertex if it opens upwards, which occurs when the coefficient 'a' (or 'p' in conic form) is positive.
  • How do you find the y-intercept of a parabola given its equation?
    To find the y-intercept of a parabola, set x = 0 in the equation and solve for y.
  • What geometric process creates a parabola in conic sections?
    A parabola is formed by slicing a three-dimensional cone with a heavily tilted two-dimensional plane. This intersection produces the characteristic parabola shape.
  • How do you determine the value of 'p' in the standard form of a parabola's equation?
    Set the coefficient in front of the linear term equal to 4p and solve for p by dividing by 4. This value helps locate the focus and directrix.
  • Where is the focus located relative to the vertex for a parabola that opens upwards?
    The focus is located above the vertex by a distance equal to the absolute value of p. This means you move up p units from the vertex.
  • For a horizontal parabola, how do you find the directrix line?
    The directrix is a vertical line located p units in the opposite direction of the parabola's opening from the vertex. Its equation is x equals the vertex's x-coordinate minus p.
  • What is the relationship between the axis of symmetry and the directrix in vertical and horizontal parabolas?
    The directrix is always perpendicular to the axis of symmetry. For vertical parabolas, the directrix is horizontal; for horizontal parabolas, the directrix is vertical.
  • How do you determine the width of a parabola when graphing it?
    From the focus, move left and right (for vertical parabolas) or up and down (for horizontal parabolas) by 2|p| units to find the width points. These points help define the parabola's shape.
  • What does a positive p value indicate about the direction a horizontal parabola opens?
    A positive p value means the horizontal parabola opens to the right. Conversely, a negative p value means it opens to the left.