Question

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

Answer 1

y=8x²+2x-5
y+5=8(x²+x/4)
y+41/8=8(x²+x/4+1/64)
y+41/8=8(x+1/8)²
f(x)=8(x+1/8)²-41/8

Answer 2

The given function is

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

Comparing with

`ax^(2)+bx+c`

We get

a = 8, b = 2 & c = -5

Now if (h,k) is the vertex

then h =
`-(b)/(2a)=-(2)/(2(8))=-(1)/(8)`

Substituting the value of h in place of x in the function we get

k=
`8(-(1)/(8))^2+2(-(1)/(8))-5 = -(41)/(8)`

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

The vertex form of f(x) = 8x² +2x-5 is

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

Answer