QUADRATIC FUNCTION

Quadratic Function

Definition Of Quadratic Function

Quadratic function is a function that can be described by an equation of the form f(x) = ax² + bx + c, where a ≠ 0.

In a quadratic function, the greatest power of the variable is 2. The graph of a quadratic function is a parabola.

More About Quadratic Function

Quadratic equation: An equation in the standard form ax² + bx + c = 0, where a ≠ 0 is called a quadratic equation.
Quadratic formula: A quadratic formula is the solution of a quadratic equation ax² + bx + c = 0, where a ≠ 0, given by
Quadratic inequality: An inequality written in one of the forms y <ax² + bx + c,
y ≥ ax² + bx + c, y ≤ ax² + bx + c, or y > ax² + bx + c is called a quadratic inequality.
Quadratic term: A term ax² is the quadratic term in the equation f(x) = ax² + bx + c

Examples of Quadratic Function

The following are few examples of quadratic functions.

Video Examples: Quadratic Functions

Solved Example on Quadratic Function

Ques: Graph the quadratic function y = - (1/4)x².Indicate whether the parabola opens up or down.

Choices:

A. Graph-A; opens down
B. Graph-B; opens down

Correct Answer: A

Solution:

Step 1: Make a table of ordered pairs for the given function.

Step 2: Plot these points on the coordinate plane and connect the points with a smooth curve.
Step 3: The graph looks like the one below

Step 4: It can be observed from the graph that the parabola opens down.
Step 5: The equation of the axis of symmetry is: x = 0
Step 6: The vertex is at (0, 0)
Step 7: The parabola opens down. So, the vertex is the maximum point.

Quick Summary

The graph of a quadratic function is a parabola.
The greatest power of the variable in a quadratic function is 2.
Quadratic functions can be expressed as quadratic equations, inequalities, or have quadratic terms.

\[ f(x) = ax^2 + bx + c \]

🍎 Teacher Insights

Emphasize the connection between the algebraic representation and the graphical representation of quadratic functions. Use real-world examples to illustrate the applications of quadratic functions.

🎓 Prerequisites

Basic algebra
Understanding of variables and coefficients
Graphing linear equations

Check Your Knowledge

Q1: Which of the following is a quadratic function?

f(x) = 2x + 1 f(x) = x^2 - 3x + 2 f(x) = 1/x f(x) = |x|

Q2: What is the shape of the graph of a quadratic function?

Line Circle Parabola Hyperbola

Frequently Asked Questions

Q: What is the difference between a quadratic function and a quadratic equation?
A: A quadratic function is an expression of the form f(x) = ax^2 + bx + c, while a quadratic equation sets that expression equal to zero: ax^2 + bx + c = 0.

Q: How do you find the vertex of a parabola?
A: The x-coordinate of the vertex is given by -b/(2a). Substitute this value into the function to find the y-coordinate.