Question

Vertex form:

F(x)= 2x^2+16x+18

Answer 1

`f(x)= 2(x+4)^2-14`

Explanation:

Hi there!

Vertex form:
`f(x)=a(x-h)^2+k`

`f(x)= 2x^2+16x+18`

Factor out 2 from the first two terms:

`f(x)= 2(x^2+8x)+18`

Complete the square inside the brackets by adding (8/2)² inside the brackets:

`f(x)= 2(x^2+8x+16)+18`

Subtract 2(16) outside the brackets (because you cannot randomly add a term):

`f(x)= 2(x^2+8x+16)+18-2(16)`

Complete the square and subtract:

`f(x)= 2(x+4)^2-14`

I hope this helps!