Complete the square on the equation (x^2)-4x-3
x2-4x-3 First factorise into squared form and expand.(x-2)2=x2-4x+4Balance the equations.x2-4x+4 needs to be x2-4x-3This leads to(x-2)2-4-3 to get rid of the +4 from factorising.Leaving finally(x-2)2-7As an extension could ask the student about minimum value of the curve
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