Question

Write the equation $y=2x^2-12x+6$ in standard form.

Short answer

The required form of the equation in standard form $y=a{\left(x-h\right)}^2+k$ is $y=2{\left(x-3\right)}^2-12$where $a=2,h=3\text{and}k=-12$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $y=2x^2-12x+6$.

Step 2. Calculation.

The given equation $y=2x^2-12x+6$ is converted to standard form $y=a{\left(x-h\right)}^2+k$ as:

$\begin{array}{c}y=2x^2-12x+6\\ =2\left(x^2-6x+3\right)\\ =2\left(x^2-6x+3+{\left(-3\right)}^2-{\left(-3\right)}^2\right)\mathrm{....}\left(\begin{array}{l}\text{Addand}\\ \text{subtract}{\left(-3\right)}^2\end{array}\right)\\ =2\left(x^2-6x+{\left(-3\right)}^2\right)+2\left(3-{\left(-3\right)}^2\right)\\ =2{\left(x-3\right)}^2-12\end{array}$

Here $a=2,h=3\text{and}k=-12$.

Step 3. Conclusion.

The required form of the given equation is $y=2{\left(x-3\right)}^2-12$ where $a=2,h=3\text{and}k=-12$.