5 Questions
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?
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?
The axis of symmetry is a line that a parabola is symmetric with respect to.
What is the vertex of a parabola?
The vertex is the point where a parabola intersects its axis of symmetry.
How many points are needed to determine a line?
Two points are needed to determine a line.
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.
Test your understanding of quadratic functions with this quiz. Explore the concepts of graphing and solving quadratic equations in this interactive quiz. Challenge yourself with a variety of problems to strengthen your skills in quadratic functions.
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