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VERTEX

# VERTEX - Year10Advanced MathematicsA4(iv Findingthevertexby...

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Year 10 Advanced  Mathematics  A4(iv) Finding the vertex by  completing the square

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e.g.   y = x 2  + 4x + 4 This factorises to…………. And therefore cuts the x-axis once at An equation which happens to be a perfect square is very easy to graph….. e.g.   y = (x + 2) 2 x = -2 With a y- intercept at y = 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x y
If these perfect square equations are written in factored form…. e.g.   y = (x + 2) 2 and then a constant is added or subtracted…... e.g.   y = (x + 2) + 2 Then it is still easy to graph, but one more bit of information is given -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 x y This time the previous graph simply moves up  2 units and the axis of symmetry has stayed in the  same place.

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Why bother understanding how to use an equation in this form?
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