Use the slider to explore worked examples.

Worked Example

Complete the square for: \(x^{2}+10x+8 \)
Worked Example

Complete the square for: \(x^{2}-8x+2=0 \)
Worked Example

Complete the square for: \(3x^{2}+12x+7=0 \)

Note: There are now more than one \(x^{2}\)
Completing the square is also a useful technique for finding the minimum or maximum value of a quadratic.

We will look at an example, to see how this is done.

Worked Example

(a) Complete the square for \(y=2x^{2} -8x+2\)

(b) Find the minimum value of \(y\)

(c) Sketch the graph of \(y=2x^{2} -8x+2\)
Here is an example, to find the maximum turning point:

Worked Example

The height of a ball thrown into the air is given by
\(h=1+20t-10t^{2}\)

Find the maximum height reached by the ball.

Quadratic Equations