Answer:
[tex]g(x)=2(x-1.75)^{2}-1.125[/tex]
Step-by-step explanation:
we have
[tex]g(x)=2x^{2} -7x+5[/tex]
Factor the leading coefficient 2
[tex]g(x)=2(x^{2} -3.5x)+5[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]g(x)=2(x^{2} -3.5x+1.75^2)+5-(2)(1.75^2)[/tex]
[tex]g(x)=2(x^{2} -3.5x+1.75^2)+5-6.125[/tex]
[tex]g(x)=2(x^{2} -3.5x+1.75^2)-1.125[/tex]
Rewrite as perfect squares
[tex]g(x)=2(x-1.75)^{2}-1.125[/tex]
