Question

Write in vertex form.y = x^2-12x+41

Answer 1

$y=(x-6)^{2}-22$

Explanation

given

$y=x^2-12x+14$

The vertex form is a special form of a quadratic function. From the vertex form, it is easily visible where the maximum or minimum point (the vertex) of the parabola is, it has the form

$\begin{gathered} y=(x-h)^2+k \\ where \\ the\text{ vertex is \lparen h,k\rparen} \end{gathered}$

Step 1

a) complete the square

$\begin{gathered} y=x^{2}-12x+14 \\ y=x^2-12x+14+(-6)^2+6^2 \\ us\text{ ethe binomial formula} \\ y=\left(x-6\right)^2-(-6^2)+6^14 \\ y=(x-6)^2-22 \end{gathered}$

so , the equation in vertex form is

$y=(x-6)^2-22$

I hope this helps you