G(x) = 2x² +16x+35
(a) Write the equation in the form g (x)= a (x - h)2 + k.

The equation   g(x) = 2(x+4)² +3

 (h,k) = (-4,3) and a = 2

Step-by-step explanation:

Step(i):-

Given equation  g(x) = 2 x² + 16 x +35

                          g(x) = 2(x² +8 x ) +35

                         g(x) = 2(x² +2(4) (x ) +(4)² -(4)²)+35

we know that (a+b)² = a²+2ab+b²

Step(ii):-

                        g(x) = 2( x+4)² - 2(16) +35

               ⇒    g(x) = 2(x+4)²  - 32 +35

              ⇒     g(x) = 2(x+4)² +3

comparing     g(x) = a (x-h)² +k

         (h,k) = (-4,3) and a = 2

Final -

The equation   g(x) = 2(x+4)² +3

 (h,k) = (-4,3) and a = 2

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: