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Questions and Answers
What is the shape of the graph of a quadratic function?
What is the shape of the graph of a quadratic function?
The graph of a quadratic function is a curve called a parabola.
What is the general form of a quadratic function?
What is the general form of a quadratic function?
The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are numbers with $a \neq 0$.
What is the axis of symmetry of a parabola?
What is the axis of symmetry of a parabola?
The axis of symmetry is a line that a parabola is symmetric with respect to.
What is the vertex of a parabola?
What is the vertex of a parabola?
How many points are needed to determine a line?
How many points are needed to determine a line?
Flashcards
Shape of a quadratic function's graph?
Shape of a quadratic function's graph?
A curve called a parabola.
General form of a quadratic function?
General form of a quadratic function?
f(x) = ax^2 + bx + c, where a, b, and c are numbers with a ≠0.
Axis of symmetry of a parabola?
Axis of symmetry of a parabola?
A line that a parabola is symmetric with respect to.
Vertex of a parabola?
Vertex of a parabola?
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Points needed to define a line?
Points needed to define a line?
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Study Notes
Quadratic Functions
- A quadratic function is a polynomial function of degree two, having the form f(x) = ax2 + bx + c, where a, b, and c are constants and a ≠0.
- The graph of a quadratic function is a curve called a parabola, which can open upward or downward and vary in width or steepness.
- Parabolas have a "U" shape and are symmetric with respect to a line called the axis of symmetry.
- The axis of symmetry intersects the parabola at a point called the vertex of the parabola.
- Two points determine a line, and there is one and only one line that contains both points.
- The x-coordinate of the vertex of a parabola can be found using the formula x = -b / 2a.
Graphs of Quadratic Functions
- The graph of a quadratic function is a parabola that opens upward or downward and has a "U" shape.
- The vertex of a parabola is the lowest or highest point on the graph.
- The axis of symmetry is the vertical line that passes through the vertex of the parabola.
- The graph of a quadratic function can be affected by the values of a, b, and c.
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