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Questions and Answers
What is a quadratic function?
What is a quadratic function?
- A constant function
- A nonlinear function written in standard form (correct)
- A linear function
- An exponential function
What is the standard form of a quadratic function?
What is the standard form of a quadratic function?
f(x) = ax^2 + bx + C, where a does not equal 0
What shape does a parabola represent?
What shape does a parabola represent?
The shape of the graph of a quadratic function
What is the axis of symmetry in a parabola?
What is the axis of symmetry in a parabola?
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What is a vertex in the context of a parabola?
What is a vertex in the context of a parabola?
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What does minimum refer to in a parabola?
What does minimum refer to in a parabola?
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What does maximum refer to in a parabola?
What does maximum refer to in a parabola?
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Study Notes
Quadratic Functions
- Nonlinear functions represented in a specific form.
- Standard form: ( f(x) = ax^2 + bx + c ) where ( a \neq 0 ).
Parabola
- The graph shape of a quadratic function, which opens either upward or downward.
Axis of Symmetry
- A vertical line that divides the parabola into two mirror-image halves.
- The equation of the axis of symmetry is given by ( x = -\frac{b}{2a} ).
Vertex
- The point where the axis of symmetry intersects the parabola.
- Represents the highest or lowest point of the graph.
Minimum
- The lowest point of the graph for a parabola that opens upward (( a > 0 )).
- At the vertex of the parabola in this case.
Maximum
- The highest point of the graph for a parabola that opens downward (( a < 0 )).
- Located at the vertex of the parabola in this situation.
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