## 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

### Examples of Quadratic Function

The following are few examples of quadratic functions.

**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*

### 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.

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