Answer:
[tex]y=8(x+\frac{1}{8} )^{2} -\frac{41}{8}[/tex]
Step-by-step explanation:
The given quadratic function is
[tex]f(x)=8x^{2} +2x-5[/tex]
Where [tex]a=8[/tex], [tex]b=2[/tex] and [tex]c=-5[/tex].
Now, let's find the vertex, which coordinates are [tex]V(h,k)[/tex], and [tex]h=-\frac{b}{2a}[/tex]
Replacing each value, we have
[tex]h=-\frac{2}{2(8)}=-\frac{1}{8}[/tex]
Then, [tex]k=f(h)[/tex], so
[tex]f(-\frac{1}{8} )=8(-\frac{1}{8} )^{2} +2(-\frac{1}{8} )-5=\frac{1}{8}-\frac{1}{4} -5=\frac{1-2-40}{8}\\ k=-\frac{41}{8}[/tex]
So, the vertex is
[tex]V(-\frac{1}{8},-\frac{41}{8})[/tex] and [tex]a=8[/tex]
Therefore, the vertex form is
[tex]y=a(x-h)^{2}+k\\ y=8(x+\frac{1}{8} )^{2} -\frac{41}{8}[/tex]
