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Questions and Answers
What is the standard form of quadratic functions?
What is the standard form of quadratic functions?
- k = (4ac - b²) / 4a
- y = ax² + bx + c (correct)
- h = -b / 2a
- y = a(x - h)² + k
What is the vertex form of a quadratic function?
What is the vertex form of a quadratic function?
- y = ax² + bx + c
- x = h
- y = a(x - h)² + k (correct)
- h = -b / 2a
What formula is used to find h in vertex form?
What formula is used to find h in vertex form?
h = -b / 2a
What formula is used to find k in vertex form?
What formula is used to find k in vertex form?
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What coordinates represent the vertex?
What coordinates represent the vertex?
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What is the axis of symmetry in a quadratic function?
What is the axis of symmetry in a quadratic function?
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A quadratic function faces upward when a < 0.
A quadratic function faces upward when a < 0.
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A quadratic function faces downward when a < 0.
A quadratic function faces downward when a < 0.
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The vertex is a minimum point when a < 0.
The vertex is a minimum point when a < 0.
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The vertex is a maximum point when a > 0.
The vertex is a maximum point when a > 0.
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Study Notes
Quadratic Functions - Standard Form
- The standard form of a quadratic function is expressed as ( y = ax^2 + bx + c ).
Quadratic Function - Vertex Form
- Vertex form is defined by the equation ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola.
Vertex Form - Formula for h
- The value of ( h ) can be calculated using the formula ( h = \frac{-b}{2a} ).
Vertex Form - Formula for k
- The value of ( k ) is determined by the formula ( k = \frac{4ac - b^2}{4a} ).
Vertex
- The vertex of a quadratic function is represented by the point ( (h, k) ), indicating the maximum or minimum of the parabola.
Axis of Symmetry
- The axis of symmetry for a quadratic function is given by the vertical line ( x = h ).
When the Quadratic Function Faces Upward
- A parabola opens upwards when the coefficient ( a ) is greater than zero ( ( a > 0 ) ).
When the Quadratic Function Faces Downward
- A parabola opens downwards when the coefficient ( a ) is less than zero ( ( a < 0 ) ).
When the Vertex is a Minimum Point
- The vertex represents a minimum point of the parabola when ( a ) is positive ( ( a > 0 ) ).
When the Vertex is a Maximum Point
- The vertex serves as a maximum point of the parabola when ( a ) is negative ( ( a < 0 ) ).
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