Introduction — lesson. Mathematics State Board, Class 10.

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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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A function is of the form

$f(x) = ax^2 + bx + c$ , where

$a$ ,

$b$ and

$c$ are constants, and

$a \neq 0$ is called a quadratic function.

Example:

The trajectory of cables in the bridge results in a parabolic path. A parabola represents a quadratic function.

A parabola is symmetric concerning a line called the axis of symmetry. The point of intersection of the parabola and the axis of symmetry is called the vertex.

Important!

For a quadratic equation, the axis is given by

$x = \frac{-b}{2a}$ and the vertex is given by

$\left(\frac{-b}{2a}, \frac{-\Delta}{4a} \right)$ where

$\Delta = b^2 - 4ac$ is the discriminant of the quadratic equation

$ax^2 + bx + c = 0$ .

A parabola usually forms a "U" shaped curve. Depending on the value of

$a$ in the general equation of the parabola

$y = ax^2$ , the parabolas open upwards or downwards and vary in width.

Let us consider the simple graph

$y = x^2$ .

Let us compare the above graph with graphs having the higher value of

$a$ .

Here, the graph

$y = x^2$ is broader than the graph

$y = 8x^2$ .

Similarly, compare graph

$y =x^2$ with graphs having lower values of

$a$ .

Here, the graph

$y = x^2$ is narrower than the graph

$y = \frac{1}{6}x^2$ .

Important!

1. The greater the value of

$a$ , the narrower is the parabola.

2. The lesser the value of

$a$ , the wider is the parabola.

Reference:

https://pixabay.com/photos/golden-gate-bridge-san-francisco-388917/

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1. Introduction

Theory: