Question

Write the equation $y=x^2-6x+11$ in standard form.

Short answer

The required form of the equation in standard form $y=a{\left(x-h\right)}^2+k$is $y={\left(x-3\right)}^2+2$ where $a=1,h=3\text{and}k=2$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $y=x^2-6x+11$.

Step 2. Calculation.

The given equation $y=x^2-6x+11$ is converted to standard form $y=a{\left(x-h\right)}^2+k$ as:

$\begin{array}{c}y=x^2-6x+11\\ =x^2-6x+11+{\left(-3\right)}^2-{\left(-3\right)}^2\mathrm{....}\left(\begin{array}{l}\text{Addand}\\ \text{subtract}{\left(-3\right)}^2\end{array}\right)\\ =\left(x^2-6x+{\left(-3\right)}^2\right)+\left(11-{\left(-3\right)}^2\right)\\ ={\left(x-3\right)}^2+2\end{array}$

Here $a=1,h=3\text{and}k=2$.

Step 3. Conclusion.

The required form of the given equation is $y={\left(x-3\right)}^2+2$ where $a=1,h=3\text{and}k=2$.