- A perfect square is formed by multiplying a quantity times itself, as in (3)(3) =9 .

Here are seven perfect squares: 25, 144, 169, (-3)

- The 'Perfect Trinomial Square' x

- When given only 2 terms such as x

The answer is to take half of the '6' to get '3' and square the '3' to get the '9'.

When you complete the square for x

Sample: if x=10, show 160=(10)

- In general, to complete the square for x

to get the 3rd term as shown here x

To complete x

- When the numerical coefficient of x

to complete the square for 2x

and then take half of the 6 and square it, to get the trinomial square 2[x

- In general, to complete the square for ax

take half of b/a and square it, (b/2a)

- Squared quantities are used in formulas for many applications: light and radiation intensity,

gravitational attraction, kinetic energy, bending strength, maximum & minimum problems...

- Completing the square can be used to find the lowest point [vertex] of a parabola such as y = x

For example, complete the square for y = x

y = x

y = (x+3)

y = (x+3)

Since the perfect square (x+3)

The vertex of this sample parabola is (-3,-1). The same parabola can be represented as y+1 = (x+3)

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