Introduction to Quadratic Function | Examples of Quadratic Function

Summary

In this video, Teacher Gone discusses quadratic functions, starting with their definition as second-degree polynomials and the requirement that the coefficient of x² (a) must not be zero. The video also covers different forms of quadratic functions, such as the standard form and vertex form, and explains the graph of a quadratic function, which is a U-shaped parabola. Teacher Gone illustrates how to identify quadratic functions from equations, tables, and graphs while comparing them to linear functions. The video is aimed at providing a clear understanding of quadratic functions and their properties.

Takeaways

• 📚 The video focuses on explaining the quadratic function, which is a second-degree polynomial.
• 🔢 A quadratic function is represented by f(x) = ax² + bx + c, or equivalently y = ax² + bx + c, where a ≠ 0.
• ❗ If a = 0, the function becomes a linear function instead of a quadratic function.
• 🔍 The graph of a quadratic function is a U-shaped curve called a parabola.
• 🧮 Quadratic functions have two main forms: standard form (f(x) = ax² + bx + c) and vertex form (f(x) = a(x-h)² + k).
• 📝 The vertex of a parabola is the highest or lowest point depending on whether the parabola opens upward or downward.
• 📏 The axis of symmetry of a parabola is a vertical line passing through the vertex, often the y-axis.
• 🔬 To determine if an equation is quadratic, the highest exponent of the variable x must be 2.
• 📊 The second difference in a table of values is constant for quadratic functions, which helps identify them.
• 📈 Quadratic functions can be recognized from their graphs (parabolas), tables of values, and equations.

Q & A

What is a quadratic function?

A quadratic function is a second-degree polynomial represented as f(x) = ax² + bx + c or y = ax² + bx + c, where a, b, and c are real numbers, and a ≠ 0.

Why should 'a' in a quadratic function not be equal to zero?

If 'a' is equal to zero, the function becomes a linear function instead of a quadratic one because it eliminates the x² term, reducing the degree of the polynomial to one.

What is the standard form of a quadratic function?

The standard form of a quadratic function is f(x) = ax² + bx + c, or equivalently, y = ax² + bx + c.

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is f(x) = a(x - h)² + k, or y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

What shape does the graph of a quadratic function take?

The graph of a quadratic function is a parabola, which is U-shaped.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves. In many cases, it corresponds to the y-axis.

How do you identify a quadratic function based on its equation?

To identify a quadratic function, check the degree of the polynomial. If the highest exponent of the variable x is 2, then the function is quadratic.

How can you determine if a function represented by a table of values is quadratic?

You can determine if a function is quadratic by calculating the first and second differences between consecutive values. If the second differences are constant, the function is quadratic.

What does the graph of a linear function look like?

The graph of a linear function is a straight line.

How can you identify a quadratic function based on its graph?

A quadratic function can be identified by its graph, which is a U-shaped curve called a parabola.