Answer:
[tex]f(x)=2(x+7)^2-103[/tex]
Step-by-step explanation:
[tex]f(x) = 2x^2+28x - 5[/tex]
To find out vertex apply the formula x=-b/2a
The value of a=2 and b=28
[tex]x=\frac{-b}{2a} =\frac{-28}{4} =-7[/tex]
Now plug in x=-7 in f(x) equation and find out f(-7)
[tex]f(-7) = 2(-7)^2+28(-7)- 5=-103[/tex]
Vertex is (-7,-103)
Now use vertex formula
[tex]f(x)=a(x-h)^2+k[/tex]
a=2, h=-7, k=-103
Plug in all the values in the vertex form equation
[tex]f(x)=2(x+7)^2-103[/tex]
