Quadratic functions worksheets

📚 Topic Summary

Quadratic functions are polynomial functions of degree 2, meaning the highest power of the variable is 2. They have a general form of $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$. The graph of a quadratic function is a parabola. Worksheets on quadratic functions usually cover topics like identifying quadratic functions, finding the vertex, axis of symmetry, roots (zeros), and sketching the graph.

These worksheets provide practice in manipulating and understanding quadratic equations, which are essential in various fields like physics, engineering, and economics.

🧠 Part A: Vocabulary

Match the term with its definition:

1. Term: Vertex
2. Term: Parabola
3. Term: Axis of Symmetry
4. Term: Quadratic Function
5. Term: Root

1. Definition: A U-shaped curve.
2. Definition: A point where the parabola changes direction.
3. Definition: A function of the form $f(x) = ax^2 + bx + c$.
4. Definition: A line that divides the parabola into two symmetrical halves.
5. Definition: The x-intercept(s) of the quadratic function.

✍️ Part B: Fill in the Blanks

A quadratic function is a polynomial of degree ____. The graph of a quadratic function is a ____. The vertex of a parabola is either a maximum or a ____ point. The axis of symmetry always passes through the ____ of the parabola. Solutions to $f(x) = 0$ are called ____.

🤔 Part C: Critical Thinking

Explain in your own words how the values of $a$, $b$, and $c$ in the quadratic equation $f(x) = ax^2 + bx + c$ affect the shape and position of the parabola. Give specific examples.