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 $4^{2}$.

$f(x)= x^{2} -2*4x+ 4^{2}- 4^{2}+3$

$f(x)=( x^{2} -2*4x+ 4^{2})- 16+3$

$f(x)=(x-4)^{2}-13$