Answer:
[tex]f(x)= 2(x+4)^2-14[/tex]
Step-by-step explanation:
Hi there!
Vertex form: [tex]f(x)=a(x-h)^2+k[/tex]
[tex]f(x)= 2x^2+16x+18[/tex]
Factor out 2 from the first two terms:
[tex]f(x)= 2(x^2+8x)+18[/tex]
Complete the square inside the brackets by adding (8/2)² inside the brackets:
[tex]f(x)= 2(x^2+8x+16)+18[/tex]
Subtract 2(16) outside the brackets (because you cannot randomly add a term):
[tex]f(x)= 2(x^2+8x+16)+18-2(16)[/tex]
Complete the square and subtract:
[tex]f(x)= 2(x+4)^2-14[/tex]
I hope this helps!
