Questions and Answers
What is the vertex form of a quadratic equation?
The graph opens down if 'a' is negative.
True
What does (h,k) represent in the vertex form?
(h,k)
What does (x,y) represent in the context of a parabola?
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A vertical stretch looks wide.
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A vertical shrink looks wide.
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The graph opens up if 'a' is positive.
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The graph moves left if 'h' is positive.
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The graph moves right if 'h' is negative.
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The graph moves up if 'k' is negative.
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The graph moves down if 'k' is negative.
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Study Notes
Vertex Form of a Parabola
- Vertex form of a quadratic equation is expressed as (y=a(x-h)^2+k).
- The parameters (h) and (k) determine the position of the vertex of the parabola.
Behavior of the Parabola
- If the coefficient (a) is negative, the graph opens downwards, indicating a maximum point at the vertex.
- If the coefficient (a) is positive, the graph opens upwards, indicating a minimum point at the vertex.
Vertex and Points on the Graph
- The vertex of the parabola is represented by the point ((h,k)).
- A specific point where the parabola intersects the graph is denoted by ((x,y)).
Width and Shape of the Parabola
- A vertical stretch occurs when the value of (a) is greater than 1, resulting in a narrower parabola.
- A vertical shrink happens when the absolute value of (a) is less than 1, producing a wider parabola.
Horizontal and Vertical Shifts
- The graph shifts left if (h) is positive in the equation, moving the vertex leftward on the Cartesian plane.
- The graph shifts right if (h) is negative, moving the vertex rightward.
- The graph shifts upward if (k) is positive, raising the vertex.
- Conversely, the graph shifts downward if (k) is negative, lowering the vertex.
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Description
Test your knowledge of the vertex form of a quadratic equation with these flashcards. This quiz covers key terms such as 'vertex,' 'graph opens down,' and the impact of 'a' on the graph's shape. Perfect for Algebra II students seeking to reinforce their understanding.
