Question

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

Answer 1

The vertex-form of a quadratic equation is
`f(x)=a(x-h)^(2)+k`, where (h, k) is the vertex of the parabola.

To complete the square of a quadratic expression in standard form, we write the coefficient of x as 2*b, then add and subtract
`b^(2)`.


`f(x)= x^(2) -8x+3`


`f(x)= x^(2) -2*4x+3`

so b=4, now add and subtract
`4^(2)`.


`f(x)= x^(2) -2*4x+ 4^(2)- 4^(2)+3`


`f(x)=( x^(2) -2*4x+ 4^(2))- 16+3`


`f(x)=(x-4)^(2)-13`