4.2 Relating The Standard And Vertex Forms: Completing The Square Worksheet With Answer Key

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4.2

Relating the Standard and Vertex Forms: Completing the Square

All quadratic functions in standard form can be written in vertex form by completing the square.

The equations are equivalent.

Both the standard form and the vertex form provide useful information for graphing the

parabola.

To complete the square of

, follow these steps:

• Factor the coefficient of from the first two terms.

• Add and subtract the square of half the coefficient of inside the brackets.

• Group the three terms that form the perfect square. Multiply the fourth term by a, and

move it outside the brackets.

• Factor the perfect square and simplify.

Any quadratic function in standard form with

can be expressed in vertex form when

fractions are used to complete the square. Decimals can be used only if the coefficient of

results in a terminating decimal when is factored from the

- and -terms of the quadratic.

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