Lesson BASICS of Quadratics

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Introduction

A quadratic is any equation of the form {{{y = ax^2 + bx + c}}}, where a, b and c are numbers.

The quadratic has to have an x-squared term, but not necessarily either of the others.

The shape of a quadratic is a symmetric curve, either U-shaped (if a is a positive number) or n-shaped (if a is a negative number), eg...

{{{graph(200,200,-5,5,-5,6,x^2-4)}}} {{{graph(200,200,-5,5,-10,2,-x^2-4)}}}

Solutions, or ROOTS

Being a curve, it will cross the x-axis either 2 times, once or never. Never more than twice. So there are always 2, 1 or zero solutions (roots) to any quadratic equation.

Where the curve turns is called the Turning Point which is either a MAXIMUM (for the n-shaped quadratic) or a MINIMUM (for the u-shaped quadratic).

The position of the turning point is always mid-way between the roots of the equation. Obviously, if the equation has just one root, then the turning point is at that value. If the equation has no roots (ie it does not cross the x-axis, then you are stuffed...you need calculus).

eof