CraigsMaths

When solving quadratic equations and sketching parabolas you can get the required points onto your graph very quickly if you know how to convert from the general form of to the standard form of . (See Standard Quadratic Form for the reasons why.) This article explains how to complete the square to acheive this.

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A parabola is a curve that is described by a quadratic equation. You may be presented with a quadratic equation in one of several forms and then asked to:

• Sketch a graph of the equation
• Find the local maxima or local minima
• Find the vertex coordinates
• Find the x-intercept(s) if they exist
• Find the the y-intercept
• Find the axis of symmetry

This article will describe the simplest approach for the different forms of the quadratic equation.

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The general quadratic form is:

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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If a quadratic can be factored it may be expressed in the following form:

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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This is the “standard” form of the quadratic equation:

where

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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