Question

Write the equation $x=y^2+14y+20$ in standard form.

Short answer

The required form of the equation in standard form$x=a{\left(y-k\right)}^2+h$is $x={\left(y+7\right)}^2-29$where $a=1,h=-29\text{and}k=-7$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $x=y^2+14y+20$.

Step 2. Calculation.

The given equation $x=y^2+14y+20$ is converted to standard form $y=a{\left(x-h\right)}^2+k$ as:

$\begin{array}{c}x=y^2+14y+20\\ =y^2+14y+20+{\left(7\right)}^2-{\left(7\right)}^2\mathrm{....}\left(\begin{array}{l}\text{Addand}\\ \text{subtract}{\left(7\right)}^2\end{array}\right)\\ =\left(y^2+14y+{\left(7\right)}^2\right)+\left(20-{\left(7\right)}^2\right)\\ ={\left(y+7\right)}^2-29\end{array}$

Here $a=1,h=-29\text{\hspace{0.33em}and}k=-7$.

Step 3. Conclusion.

The required form of the given equation is $x={\left(y+7\right)}^2-29$ where$a=1,h=-29\text{and}k=-7.$