Question

Can anyone solve this 20 points question please.

Answer 1

`g(x)=2(x-1.75)^(2)-1.125`

Explanation:

we have

`g(x)=2x^(2) -7x+5`

Factor the leading coefficient 2

`g(x)=2(x^(2) -3.5x)+5`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`g(x)=2(x^(2) -3.5x+1.75^2)+5-(2)(1.75^2)`

`g(x)=2(x^(2) -3.5x+1.75^2)+5-6.125`

`g(x)=2(x^(2) -3.5x+1.75^2)-1.125`

Rewrite as perfect squares

`g(x)=2(x-1.75)^(2)-1.125`