Question

Katie is finding the standard form of the equation of the parabola $y=x^2+6x+4$. What mistake did she make in her work.

Short answer

The mistake done is that she did not subtract 9 from the original equation.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $y=x^2+6x+4$. And the work done to covert this equation to standard form is shown below.

Step 2. Calculation.

Converting the given equation $y=x^2+6x+4$ to standard form $y=a{\left(x-h\right)}^2+k$.

$\begin{array}{c}y=x^2+6x+\mathrm{4....}\left(\text{Given}\right)\\ y=x^2+6x+4+{\left(3\right)}^2-{\left(3\right)}^2\mathrm{....}\left(\text{Addandsubtract}{\left(3\right)}^2\right)\\ y=\left(x^2+6x+{\left(3\right)}^2\right)+\left(4-{\left(3\right)}^2\right)\\ y={\left(x+3\right)}^2+\left(-5\right)\\ y={\left(x+3\right)}^2-5\end{array}$

Step 3. Conclusion.

From the calculation, it is found that she forgot to subtract 9 in the original equation because she added 9 in the original equation. Hence the mistake she made in her work is that she forget to subtract 9 to balance the equation.