## Related Words

# Quadratic Function

## Definition of Quadratic Function

Quadratic function is a function that can be described by an equation of the form
f(x) = ax^{2} + 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 *a**x*^{2}
+ *bx* + *c* = 0, where *a* ≠ 0 is called a quadratic equation.

**Quadratic formula:** A quadratic formula is the solution of a quadratic
equation *a**x*^{2} + *bx* + *c* = 0, where
*a* ≠ 0, given by

**Quadratic inequality:** An inequality written in one of the forms
*y* <*a**x*^{2} + *bx* + *c*,

*y* ≥ *a**x*^{2} + *bx* + *c*, *y*
≤ *a**x*^{2} + *bx* + *c*, or *y* >
*a**x*^{2} + *bx* + *c* is called a quadratic
inequality.

**Quadratic term:** A term *a**x*^{2} is
the quadratic term in the equation *f*(*x*) = *a**x*^{2}
+ *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)x^{2}.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.