Question

Write the equation $y=x^2+6x+9$ in the form $y=a{\left(x-h\right)}^2+k$.

Short answer

The required form of the equation in$y=a{\left(x-h\right)}^2+k$ is$y={\left(x+3\right)}^2$where$a=1,h=-3\text{and}k=0$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is$y=x^2+6x+9$.

Step 2. Calculation.

The given equation $y=x^2+6x+9$ is converted to $y=a{\left(x-h\right)}^2+k$ form as:

$\begin{array}{c}y=x^2+6x+9\\ ={\left(x\right)}^2+2\times x\times 3+{\left(3\right)}^2\\ ={\left(x+3\right)}^2\\ =1{\left(x-\left(-3\right)\right)}^2+\left(0\right)\end{array}$

Here $a=1,h=-3\text{and}k=0$.

Step 3. Conclusion.

The required form of the given equation is $y={\left(x+3\right)}^2$ where $a=1,h=-3\text{and}k=0$.