Question

Write the quadratic function in vertex form: f(x) = 8x2 + 2x - 5

Answer 1

hello :
f(x) = 8x² + 2x - 5
f(x) = 8(x²+1/4 x)-5
f(x) = 8(x²+2(1/8)x +(1/8)² -(1/8)² ) -5
f(x) = 8((x+1/8)²-1/8-5
f(x) = 8(x+1/8)²-41/5....(vertex form)

Answer 2

`y=8(x+(1)/(8) )^(2) -(41)/(8)`

Explanation:

The given quadratic function is

`f(x)=8x^(2) +2x-5`

Where
`a=8`,
`b=2` and
`c=-5`.

Now, let's find the vertex, which coordinates are
`V(h,k)`, and
`h=-(b)/(2a)`

Replacing each value, we have

`h=-(2)/(2(8))=-(1)/(8)`

Then,
`k=f(h)`, so

`f(-(1)/(8) )=8(-(1)/(8) )^(2) +2(-(1)/(8) )-5=(1)/(8)-(1)/(4) -5=(1-2-40)/(8)\\ k=-(41)/(8)`

So, the vertex is

`V(-(1)/(8),-(41)/(8))` and
`a=8`

Therefore, the vertex form is

`y=a(x-h)^(2)+k\\ y=8(x+(1)/(8) )^(2) -(41)/(8)`