Completing the square Part A

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Completing the square - Part A

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Objective To take a quadratic equation in the
form of and re-arrange it in
the form of .
This is known as completing the square. By
re-arranging an expression or equation we will be
able to graph the function, or find inverses of
quadratics.
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Rearranging quadratic equation in the form
where a1.
1. Introduce an sign and then eliminate c from
the left hand side.
2. Write down the value of and and ,
keeping your values as fractions.
3. Add to both sides of the equation.
4. The left and side will now factorise into
.
5. Eliminate the number from the right hand side
and get rid of the sign you introduced in 1.
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Rearranging quadratic equation in the form
where a is not equal to 1.
1. Take the factor of a, out of your expression,
keeping your answers as fractions.
2. Discard a for now. We will use it later.
Treat the inside of your bracket as an expression
and use the same method as before.
3. Introduce an sign and then eliminate c from
the left hand side.
4. Write down the value of and and ,
keeping your values as fractions.
5. Add to both sides of the equation.
6. The left and side will now factorise into
.
7. Eliminate the number from the right hand side
and get rid of the sign.
8. Now multiply the equation out by a as shown in
the example.
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Complete the worksheet Completing the Square A.
Continue to the Completing the Square B
worksheet, before going onto Square B slideshow.