Question

Vertex form:

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

Answer 1

Answer:

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

Step-by-step 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!