The given function is
f(x) = [tex] 8x^{2}+2x-5 [/tex]
Comparing with
[tex] ax^{2}+bx+c [/tex]
We get
a = 8, b = 2 & c = -5
Now if (h,k) is the vertex
then h =[tex] -\frac{b}{2a}=-\frac{2}{2(8)}=-\frac{1}{8} [/tex]
Substituting the value of h in place of x in the function we get
k=[tex] 8(-\frac{1}{8})^2+2(-\frac{1}{8})-5 = -\frac{41}{8} [/tex]
Now the vertex form of a quadratic equation is
f(x)= a(x-h)² + k
Substituting the values of a, h & k we get
f(x) = 8[tex] 8(x-(-\frac{1}{8}))^2+(-\frac{41}{8}) [/tex]
The vertex form of f(x) = 8x² +2x-5 is
f(x) = [tex] 8(x+\frac{1}{8})^2-\frac{41}{8} [/tex]
Answer
